Best Known (168, 192, s)-Nets in Base 2
(168, 192, 5461)-Net over F2 — Constructive and digital
Digital (168, 192, 5461)-net over F2, using
- net defined by OOA [i] based on linear OOA(2192, 5461, F2, 24, 24) (dual of [(5461, 24), 130872, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(2192, 65532, F2, 24) (dual of [65532, 65340, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2192, 65536, F2, 24) (dual of [65536, 65344, 25]-code), using
- 1 times truncation [i] based on linear OA(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, 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(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2192, 65536, F2, 24) (dual of [65536, 65344, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(2192, 65532, F2, 24) (dual of [65532, 65340, 25]-code), using
(168, 192, 10922)-Net over F2 — Digital
Digital (168, 192, 10922)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2192, 10922, F2, 6, 24) (dual of [(10922, 6), 65340, 25]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2192, 65532, F2, 24) (dual of [65532, 65340, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(2192, 65536, F2, 24) (dual of [65536, 65344, 25]-code), using
- 1 times truncation [i] based on linear OA(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 232−1, 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(2193, 65537, F2, 25) (dual of [65537, 65344, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(2192, 65536, F2, 24) (dual of [65536, 65344, 25]-code), using
- OOA 6-folding [i] based on linear OA(2192, 65532, F2, 24) (dual of [65532, 65340, 25]-code), using
(168, 192, 346592)-Net in Base 2 — Upper bound on s
There is no (168, 192, 346593)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 6277 165913 774736 808951 852166 840415 666062 431597 090807 990712 > 2192 [i]