Best Known (198, 198+19, s)-Nets in Base 2
(198, 198+19, 932069)-Net over F2 — Constructive and digital
Digital (198, 217, 932069)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (189, 208, 932066)-net over F2, using
- net defined by OOA [i] based on linear OOA(2208, 932066, F2, 19, 19) (dual of [(932066, 19), 17709046, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2208, 8388595, F2, 19) (dual of [8388595, 8388387, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(2208, 8388595, F2, 19) (dual of [8388595, 8388387, 20]-code), using
- net defined by OOA [i] based on linear OOA(2208, 932066, F2, 19, 19) (dual of [(932066, 19), 17709046, 20]-NRT-code), using
- digital (0, 9, 3)-net over F2, using
(198, 198+19, 1198374)-Net over F2 — Digital
Digital (198, 217, 1198374)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2217, 1198374, F2, 7, 19) (dual of [(1198374, 7), 8388401, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(29, 3, F2, 7, 9) (dual of [(3, 7), 12, 10]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(7;12,2) [i]
- linear OOA(2208, 1198371, F2, 7, 19) (dual of [(1198371, 7), 8388389, 20]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2208, 8388597, F2, 19) (dual of [8388597, 8388389, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 7-folding [i] based on linear OA(2208, 8388597, F2, 19) (dual of [8388597, 8388389, 20]-code), using
- linear OOA(29, 3, F2, 7, 9) (dual of [(3, 7), 12, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
(198, 198+19, large)-Net in Base 2 — Upper bound on s
There is no (198, 217, large)-net in base 2, because
- 17 times m-reduction [i] would yield (198, 200, large)-net in base 2, but