Best Known (33, 33+13, s)-Nets in Base 128
(33, 33+13, 349783)-Net over F128 — Constructive and digital
Digital (33, 46, 349783)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 9, 258)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 3, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (0, 6, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128 (see above)
- digital (0, 3, 129)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (24, 37, 349525)-net over F128, using
- net defined by OOA [i] based on linear OOA(12837, 349525, F128, 13, 13) (dual of [(349525, 13), 4543788, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(12837, 2097151, F128, 13) (dual of [2097151, 2097114, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using
- an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(12837, 2097152, F128, 13) (dual of [2097152, 2097115, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(12837, 2097151, F128, 13) (dual of [2097151, 2097114, 14]-code), using
- net defined by OOA [i] based on linear OOA(12837, 349525, F128, 13, 13) (dual of [(349525, 13), 4543788, 14]-NRT-code), using
- digital (3, 9, 258)-net over F128, using
(33, 33+13, 1398100)-Net in Base 128 — Constructive
(33, 46, 1398100)-net in base 128, using
- 1283 times duplication [i] based on (30, 43, 1398100)-net in base 128, using
- net defined by OOA [i] based on OOA(12843, 1398100, S128, 13, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(12843, 8388601, S128, 13), using
- discarding factors based on OA(12843, large, S128, 13), using
- discarding parts of the base [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,12], and designed minimum distance d ≥ |I|+1 = 14 [i]
- discarding parts of the base [i] based on linear OA(25637, large, F256, 13) (dual of [large, large−37, 14]-code), using
- discarding factors based on OA(12843, large, S128, 13), using
- OOA 6-folding and stacking with additional row [i] based on OA(12843, 8388601, S128, 13), using
- net defined by OOA [i] based on OOA(12843, 1398100, S128, 13, 13), using
(33, 33+13, 4979623)-Net over F128 — Digital
Digital (33, 46, 4979623)-net over F128, using
(33, 33+13, large)-Net in Base 128 — Upper bound on s
There is no (33, 46, large)-net in base 128, because
- 11 times m-reduction [i] would yield (33, 35, large)-net in base 128, but