Best Known (221−19, 221, s)-Nets in Base 2
(221−19, 221, 932074)-Net over F2 — Constructive and digital
Digital (202, 221, 932074)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (4, 13, 8)-net over F2, using
- net from sequence [i] based on digital (4, 7)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (4, 7)-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 (4, 13, 8)-net over F2, using
(221−19, 221, 1308609)-Net over F2 — Digital
Digital (202, 221, 1308609)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2221, 1308609, F2, 6, 19) (dual of [(1308609, 6), 7851433, 20]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2221, 1398108, F2, 6, 19) (dual of [(1398108, 6), 8388427, 20]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(213, 8, F2, 6, 9) (dual of [(8, 6), 35, 10]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,38P) [i] based on function field F/F2 with g(F) = 4 and N(F) ≥ 8, using
- linear OOA(2208, 1398100, F2, 6, 19) (dual of [(1398100, 6), 8388392, 20]-NRT-code), using
- OOA 6-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 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 6-folding [i] based on linear OA(2208, 8388600, F2, 19) (dual of [8388600, 8388392, 20]-code), using
- linear OOA(213, 8, F2, 6, 9) (dual of [(8, 6), 35, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- discarding factors / shortening the dual code based on linear OOA(2221, 1398108, F2, 6, 19) (dual of [(1398108, 6), 8388427, 20]-NRT-code), using
(221−19, 221, large)-Net in Base 2 — Upper bound on s
There is no (202, 221, large)-net in base 2, because
- 17 times m-reduction [i] would yield (202, 204, large)-net in base 2, but