Best Known (22, 22+15, s)-Nets in Base 128
(22, 22+15, 2490)-Net over F128 — Constructive and digital
Digital (22, 37, 2490)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 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 (14, 29, 2340)-net over F128, using
- net defined by OOA [i] based on linear OOA(12829, 2340, F128, 15, 15) (dual of [(2340, 15), 35071, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12829, 16381, F128, 15) (dual of [16381, 16352, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using
- an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(12829, 16384, F128, 15) (dual of [16384, 16355, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(12829, 16381, F128, 15) (dual of [16381, 16352, 16]-code), using
- net defined by OOA [i] based on linear OOA(12829, 2340, F128, 15, 15) (dual of [(2340, 15), 35071, 16]-NRT-code), using
- digital (1, 8, 150)-net over F128, using
(22, 22+15, 9363)-Net in Base 128 — Constructive
(22, 37, 9363)-net in base 128, using
- 1282 times duplication [i] based on (20, 35, 9363)-net in base 128, using
- net defined by OOA [i] based on OOA(12835, 9363, S128, 15, 15), using
- OOA 7-folding and stacking with additional row [i] based on OA(12835, 65542, S128, 15), using
- discarding parts of the base [i] based on linear OA(25630, 65542, F256, 15) (dual of [65542, 65512, 16]-code), using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- linear OA(25629, 65537, F256, 15) (dual of [65537, 65508, 16]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,7], and minimum distance d ≥ |{−7,−6,…,7}|+1 = 16 (BCH-bound) [i]
- linear OA(25625, 65537, F256, 13) (dual of [65537, 65512, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- linear OA(2561, 5, F256, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(2561, s, F256, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,7]) ⊂ C([0,6]) [i] based on
- discarding parts of the base [i] based on linear OA(25630, 65542, F256, 15) (dual of [65542, 65512, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on OA(12835, 65542, S128, 15), using
- net defined by OOA [i] based on OOA(12835, 9363, S128, 15, 15), using
(22, 22+15, 17656)-Net over F128 — Digital
Digital (22, 37, 17656)-net over F128, using
(22, 22+15, large)-Net in Base 128 — Upper bound on s
There is no (22, 37, large)-net in base 128, because
- 13 times m-reduction [i] would yield (22, 24, large)-net in base 128, but