Best Known (96−12, 96, s)-Nets in Base 2
(96−12, 96, 10922)-Net over F2 — Constructive and digital
Digital (84, 96, 10922)-net over F2, using
- net defined by OOA [i] based on linear OOA(296, 10922, F2, 12, 12) (dual of [(10922, 12), 130968, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(296, 65532, F2, 12) (dual of [65532, 65436, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(296, 65536, F2, 12) (dual of [65536, 65440, 13]-code), using
- 1 times truncation [i] based on linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(296, 65536, F2, 12) (dual of [65536, 65440, 13]-code), using
- OA 6-folding and stacking [i] based on linear OA(296, 65532, F2, 12) (dual of [65532, 65436, 13]-code), using
(96−12, 96, 16384)-Net over F2 — Digital
Digital (84, 96, 16384)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(296, 16384, F2, 4, 12) (dual of [(16384, 4), 65440, 13]-NRT-code), using
- OOA 4-folding [i] based on linear OA(296, 65536, F2, 12) (dual of [65536, 65440, 13]-code), using
- 1 times truncation [i] based on linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(297, 65537, F2, 13) (dual of [65537, 65440, 14]-code), using
- OOA 4-folding [i] based on linear OA(296, 65536, F2, 12) (dual of [65536, 65440, 13]-code), using
(96−12, 96, 196192)-Net in Base 2 — Upper bound on s
There is no (84, 96, 196193)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 79228 501405 269736 098499 953040 > 296 [i]