Best Known (190, 190+19, s)-Nets in Base 2
(190, 190+19, 932066)-Net over F2 — Constructive and digital
Digital (190, 209, 932066)-net over F2, using
- 21 times duplication [i] based on 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
(190, 190+19, 1198371)-Net over F2 — Digital
Digital (190, 209, 1198371)-net over F2, using
- 21 times duplication [i] based on digital (189, 208, 1198371)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on 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
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2208, 1198371, F2, 7, 19) (dual of [(1198371, 7), 8388389, 20]-NRT-code), using
(190, 190+19, large)-Net in Base 2 — Upper bound on s
There is no (190, 209, large)-net in base 2, because
- 17 times m-reduction [i] would yield (190, 192, large)-net in base 2, but