Best Known (59−12, 59, s)-Nets in Base 32
(59−12, 59, 1398100)-Net over F32 — Constructive and digital
Digital (47, 59, 1398100)-net over F32, using
- 323 times duplication [i] based on 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
(59−12, 59, large)-Net over F32 — Digital
Digital (47, 59, large)-net over F32, using
- 323 times duplication [i] based on digital (44, 56, large)-net over F32, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] 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]
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3256, large, F32, 12) (dual of [large, large−56, 13]-code), using
(59−12, 59, large)-Net in Base 32 — Upper bound on s
There is no (47, 59, large)-net in base 32, because
- 10 times m-reduction [i] would yield (47, 49, large)-net in base 32, but