Best Known (132, 132+24, s)-Nets in Base 2
(132, 132+24, 682)-Net over F2 — Constructive and digital
Digital (132, 156, 682)-net over F2, using
- net defined by OOA [i] based on linear OOA(2156, 682, F2, 24, 24) (dual of [(682, 24), 16212, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2156, 8184, F2, 24) (dual of [8184, 8028, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2156, 8192, F2, 24) (dual of [8192, 8036, 25]-code), using
- 1 times truncation [i] based on linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2156, 8192, F2, 24) (dual of [8192, 8036, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2156, 8184, F2, 24) (dual of [8184, 8028, 25]-code), using
(132, 132+24, 2002)-Net over F2 — Digital
Digital (132, 156, 2002)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2156, 2002, F2, 4, 24) (dual of [(2002, 4), 7852, 25]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2156, 2048, F2, 4, 24) (dual of [(2048, 4), 8036, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2156, 8192, F2, 24) (dual of [8192, 8036, 25]-code), using
- 1 times truncation [i] based on linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8193 | 226−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(2157, 8193, F2, 25) (dual of [8193, 8036, 26]-code), using
- OOA 4-folding [i] based on linear OA(2156, 8192, F2, 24) (dual of [8192, 8036, 25]-code), using
- discarding factors / shortening the dual code based on linear OOA(2156, 2048, F2, 4, 24) (dual of [(2048, 4), 8036, 25]-NRT-code), using
(132, 132+24, 43308)-Net in Base 2 — Upper bound on s
There is no (132, 156, 43309)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 91349 450750 406918 701825 053654 929259 562820 174037 > 2156 [i]