Best Known (63−12, 63, s)-Nets in Base 32
(63−12, 63, 1398144)-Net over F32 — Constructive and digital
Digital (51, 63, 1398144)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (1, 7, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (44, 56, 1398100)-net over F32, using
- net defined by OOA [i] based on linear OOA(3256, 1398100, F32, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3256, 8388600, F32, 12) (dual of [8388600, 8388544, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3256, large, F32, 12) (dual of [large, large−56, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(3256, large, F32, 12) (dual of [large, large−56, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(3256, 8388600, F32, 12) (dual of [8388600, 8388544, 13]-code), using
- net defined by OOA [i] based on linear OOA(3256, 1398100, F32, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
- digital (1, 7, 44)-net over F32, using
(63−12, 63, 1398229)-Net in Base 32 — Constructive
(51, 63, 1398229)-net in base 32, using
- base change [i] based on (33, 45, 1398229)-net in base 128, using
- (u, u+v)-construction [i] based on
- digital (0, 6, 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
- (27, 39, 1398100)-net in base 128, using
- net defined by OOA [i] based on OOA(12839, 1398100, S128, 12, 12), using
- OA 6-folding and stacking [i] based on OA(12839, 8388600, S128, 12), using
- discarding factors based on OA(12839, large, S128, 12), using
- discarding parts of the base [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,11], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding parts of the base [i] based on linear OA(25634, large, F256, 12) (dual of [large, large−34, 13]-code), using
- discarding factors based on OA(12839, large, S128, 12), using
- OA 6-folding and stacking [i] based on OA(12839, 8388600, S128, 12), using
- net defined by OOA [i] based on OOA(12839, 1398100, S128, 12, 12), using
- digital (0, 6, 129)-net over F128, using
- (u, u+v)-construction [i] based on
(63−12, 63, large)-Net over F32 — Digital
Digital (51, 63, large)-net over F32, using
- 322 times duplication [i] based on digital (49, 61, large)-net over F32, using
- t-expansion [i] based on digital (48, 61, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3261, large, F32, 13) (dual of [large, large−61, 14]-code), using
- t-expansion [i] based on digital (48, 61, large)-net over F32, using
(63−12, 63, large)-Net in Base 32 — Upper bound on s
There is no (51, 63, large)-net in base 32, because
- 10 times m-reduction [i] would yield (51, 53, large)-net in base 32, but