Best Known (18−7, 18, s)-Nets in Base 128
(18−7, 18, 16554)-Net over F128 — Constructive and digital
Digital (11, 18, 16554)-net over F128, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 0, 129)-net over F128, using
- s-reduction based on digital (0, 0, s)-net over F128 with arbitrarily large s, using
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 0, 129)-net over F128 (see above)
- digital (0, 1, 129)-net over F128, using
- s-reduction based on digital (0, 1, s)-net over F128 with arbitrarily large s, using
- digital (0, 1, 129)-net over F128 (see above)
- digital (0, 1, 129)-net over F128 (see above)
- digital (0, 1, 129)-net over F128 (see above)
- digital (0, 2, 129)-net over F128, using
- digital (1, 4, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (1, 8, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128 (see above)
- digital (0, 0, 129)-net over F128, using
(18−7, 18, 21974)-Net in Base 128 — Constructive
(11, 18, 21974)-net in base 128, using
- net defined by OOA [i] based on OOA(12818, 21974, S128, 9, 7), using
- OOA stacking with additional row [i] based on OOA(12818, 21975, S128, 3, 7), using
- (u, u+v)-construction [i] based on
- linear OOA(1283, 129, F128, 3, 3) (dual of [(129, 3), 384, 4]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;384,128) [i]
- OOA(12815, 21846, S128, 3, 7), using
- OOA 3-folding [i] based on OA(12815, 65538, S128, 7), using
- discarding parts of the base [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(25613, 65536, F256, 7) (dual of [65536, 65523, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(25611, 65536, F256, 6) (dual of [65536, 65525, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding parts of the base [i] based on linear OA(25613, 65538, F256, 7) (dual of [65538, 65525, 8]-code), using
- OOA 3-folding [i] based on OA(12815, 65538, S128, 7), using
- linear OOA(1283, 129, F128, 3, 3) (dual of [(129, 3), 384, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on OOA(12818, 21975, S128, 3, 7), using
(18−7, 18, 49440)-Net over F128 — Digital
Digital (11, 18, 49440)-net over F128, using
(18−7, 18, 56539)-Net in Base 128
(11, 18, 56539)-net in base 128, using
- net defined by OOA [i] based on OOA(12818, 56539, S128, 9, 7), using
- OOA stacking with additional row [i] based on OOA(12818, 56540, S128, 3, 7), using
- discarding parts of the base [i] based on linear OOA(25615, 56540, F256, 3, 7) (dual of [(56540, 3), 169605, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25615, 56540, F256, 7) (dual of [56540, 56525, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(25615, 65540, F256, 7) (dual of [65540, 65525, 8]-code), using
- construction X applied to C([0,3]) ⊂ C([1,3]) [i] based on
- linear OA(25613, 65537, F256, 7) (dual of [65537, 65524, 8]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,3], and minimum distance d ≥ |{−3,−2,…,3}|+1 = 8 (BCH-bound) [i]
- linear OA(25612, 65537, F256, 4) (dual of [65537, 65525, 5]-code), using the narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [1,3], and minimum distance d ≥ |{−3,−1,1,3}|+1 = 5 (BCH-bound) [i]
- linear OA(2562, 3, F256, 2) (dual of [3, 1, 3]-code or 3-arc in PG(1,256)), using
- dual of repetition code with length 3 [i]
- construction X applied to C([0,3]) ⊂ C([1,3]) [i] based on
- discarding factors / shortening the dual code based on linear OA(25615, 65540, F256, 7) (dual of [65540, 65525, 8]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25615, 56540, F256, 7) (dual of [56540, 56525, 8]-code), using
- discarding parts of the base [i] based on linear OOA(25615, 56540, F256, 3, 7) (dual of [(56540, 3), 169605, 8]-NRT-code), using
- OOA stacking with additional row [i] based on OOA(12818, 56540, S128, 3, 7), using
(18−7, 18, large)-Net in Base 128 — Upper bound on s
There is no (11, 18, large)-net in base 128, because
- 5 times m-reduction [i] would yield (11, 13, large)-net in base 128, but