Best Known (168−14, 168, s)-Nets in Base 2
(168−14, 168, 1198374)-Net over F2 — Constructive and digital
Digital (154, 168, 1198374)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (0, 7, 3)-net over F2, using
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 0 and N(F) ≥ 3, using
- the rational function field F2(x) [i]
- Niederreiter sequence [i]
- Sobol sequence [i]
- net from sequence [i] based on digital (0, 2)-sequence over F2, using
- digital (147, 161, 1198371)-net over F2, using
- net defined by OOA [i] based on linear OOA(2161, 1198371, F2, 14, 14) (dual of [(1198371, 14), 16777033, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2161, 8388597, F2, 14) (dual of [8388597, 8388436, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2161, 8388597, F2, 14) (dual of [8388597, 8388436, 15]-code), using
- net defined by OOA [i] based on linear OOA(2161, 1198371, F2, 14, 14) (dual of [(1198371, 14), 16777033, 15]-NRT-code), using
- digital (0, 7, 3)-net over F2, using
(168−14, 168, 1677723)-Net over F2 — Digital
Digital (154, 168, 1677723)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2168, 1677723, F2, 5, 14) (dual of [(1677723, 5), 8388447, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(27, 3, F2, 5, 7) (dual of [(3, 5), 8, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(5;8,2) [i]
- linear OOA(2161, 1677720, F2, 5, 14) (dual of [(1677720, 5), 8388439, 15]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OOA 5-folding [i] based on linear OA(2161, 8388600, F2, 14) (dual of [8388600, 8388439, 15]-code), using
- linear OOA(27, 3, F2, 5, 7) (dual of [(3, 5), 8, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(168−14, 168, large)-Net in Base 2 — Upper bound on s
There is no (154, 168, large)-net in base 2, because
- 12 times m-reduction [i] would yield (154, 156, large)-net in base 2, but