Best Known (196−27, 196, s)-Nets in Base 2
(196−27, 196, 2520)-Net over F2 — Constructive and digital
Digital (169, 196, 2520)-net over F2, using
- net defined by OOA [i] based on linear OOA(2196, 2520, F2, 27, 27) (dual of [(2520, 27), 67844, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2196, 32761, F2, 27) (dual of [32761, 32565, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(2196, 32761, F2, 27) (dual of [32761, 32565, 28]-code), using
(196−27, 196, 5461)-Net over F2 — Digital
Digital (169, 196, 5461)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2196, 5461, F2, 6, 27) (dual of [(5461, 6), 32570, 28]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2196, 32766, F2, 27) (dual of [32766, 32570, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 215−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using
- OOA 6-folding [i] based on linear OA(2196, 32766, F2, 27) (dual of [32766, 32570, 28]-code), using
(196−27, 196, 185699)-Net in Base 2 — Upper bound on s
There is no (169, 196, 185700)-net in base 2, because
- 1 times m-reduction [i] would yield (169, 195, 185700)-net in base 2, but
- the generalized Rao bound for nets shows that 2m ≥ 50217 146618 839318 865882 738111 221123 854146 492347 065804 341576 > 2195 [i]