Best Known (49, 49+14, s)-Nets in Base 2
(49, 49+14, 102)-Net over F2 — Constructive and digital
Digital (49, 63, 102)-net over F2, using
- trace code for nets [i] based on digital (7, 21, 34)-net over F8, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 7 and N(F) ≥ 34, using
- net from sequence [i] based on digital (7, 33)-sequence over F8, using
(49, 49+14, 214)-Net over F2 — Digital
Digital (49, 63, 214)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(263, 214, F2, 2, 14) (dual of [(214, 2), 365, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(263, 255, F2, 2, 14) (dual of [(255, 2), 447, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(263, 510, F2, 14) (dual of [510, 447, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(263, 511, F2, 14) (dual of [511, 448, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 511 = 29−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(263, 511, F2, 14) (dual of [511, 448, 15]-code), using
- OOA 2-folding [i] based on linear OA(263, 510, F2, 14) (dual of [510, 447, 15]-code), using
- discarding factors / shortening the dual code based on linear OOA(263, 255, F2, 2, 14) (dual of [(255, 2), 447, 15]-NRT-code), using
(49, 49+14, 1720)-Net in Base 2 — Upper bound on s
There is no (49, 63, 1721)-net in base 2, because
- the generalized Rao bound for nets shows that 2m ≥ 9 238562 868873 498624 > 263 [i]