Best Known (154, 169, s)-Nets in Base 2
(154, 169, 1198374)-Net over F2 — Constructive and digital
Digital (154, 169, 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, 162, 1198371)-net over F2, using
- net defined by OOA [i] based on linear OOA(2162, 1198371, F2, 15, 15) (dual of [(1198371, 15), 17975403, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- net defined by OOA [i] based on linear OOA(2162, 1198371, F2, 15, 15) (dual of [(1198371, 15), 17975403, 16]-NRT-code), using
- digital (0, 7, 3)-net over F2, using
(154, 169, 1398103)-Net over F2 — Digital
Digital (154, 169, 1398103)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2169, 1398103, F2, 6, 15) (dual of [(1398103, 6), 8388449, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(27, 3, F2, 6, 7) (dual of [(3, 6), 11, 8]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(6;11,2) [i]
- linear OOA(2162, 1398100, F2, 6, 15) (dual of [(1398100, 6), 8388438, 16]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 6-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- linear OOA(27, 3, F2, 6, 7) (dual of [(3, 6), 11, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(154, 169, large)-Net in Base 2 — Upper bound on s
There is no (154, 169, large)-net in base 2, because
- 13 times m-reduction [i] would yield (154, 156, large)-net in base 2, but