Best Known (31, 31+13, s)-Nets in Base 128
(31, 31+13, 349675)-Net over F128 — Constructive and digital
Digital (31, 44, 349675)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 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 (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 (1, 7, 150)-net over F128, using
(31, 31+13, 1398100)-Net in Base 128 — Constructive
(31, 44, 1398100)-net in base 128, using
- 1281 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
(31, 31+13, 2218173)-Net over F128 — Digital
Digital (31, 44, 2218173)-net over F128, using
(31, 31+13, large)-Net in Base 128 — Upper bound on s
There is no (31, 44, large)-net in base 128, because
- 11 times m-reduction [i] would yield (31, 33, large)-net in base 128, but