Best Known (169, 169+26, s)-Nets in Base 2
(169, 169+26, 2520)-Net over F2 — Constructive and digital
Digital (169, 195, 2520)-net over F2, using
- net defined by OOA [i] based on linear OOA(2195, 2520, F2, 26, 26) (dual of [(2520, 26), 65325, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(2195, 32760, F2, 26) (dual of [32760, 32565, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2195, 32767, F2, 26) (dual of [32767, 32572, 27]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2195, 32767, F2, 26) (dual of [32767, 32572, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(2195, 32760, F2, 26) (dual of [32760, 32565, 27]-code), using
(169, 169+26, 5984)-Net over F2 — Digital
Digital (169, 195, 5984)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2195, 5984, F2, 5, 26) (dual of [(5984, 5), 29725, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2195, 6553, F2, 5, 26) (dual of [(6553, 5), 32570, 27]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2195, 32765, F2, 26) (dual of [32765, 32570, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2195, 32767, F2, 26) (dual of [32767, 32572, 27]-code), using
- 1 times truncation [i] 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]
- 1 times truncation [i] based on linear OA(2196, 32768, F2, 27) (dual of [32768, 32572, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(2195, 32767, F2, 26) (dual of [32767, 32572, 27]-code), using
- OOA 5-folding [i] based on linear OA(2195, 32765, F2, 26) (dual of [32765, 32570, 27]-code), using
- discarding factors / shortening the dual code based on linear OOA(2195, 6553, F2, 5, 26) (dual of [(6553, 5), 32570, 27]-NRT-code), using
(169, 169+26, 185699)-Net in Base 2 — Upper bound on s
There is no (169, 195, 185700)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 50217 146618 839318 865882 738111 221123 854146 492347 065804 341576 > 2195 [i]