Best Known (96, 96+9, s)-Nets in Base 2
(96, 96+9, 2097215)-Net over F2 — Constructive and digital
Digital (96, 105, 2097215)-net over F2, using
- net defined by OOA [i] based on linear OOA(2105, 2097215, F2, 9, 9) (dual of [(2097215, 9), 18874830, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2105, 2097215, F2, 8, 9) (dual of [(2097215, 8), 16777615, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(212, 65, F2, 8, 4) (dual of [(65, 8), 508, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(212, 65, F2, 4, 4) (dual of [(65, 4), 248, 5]-NRT-code), using
- appending kth column [i] based on linear OOA(212, 65, F2, 3, 4) (dual of [(65, 3), 183, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 12, 65)-net over F2, using
- appending kth column [i] based on linear OOA(212, 65, F2, 3, 4) (dual of [(65, 3), 183, 5]-NRT-code), using
- appending 4 arbitrary columns [i] based on linear OOA(212, 65, F2, 4, 4) (dual of [(65, 4), 248, 5]-NRT-code), using
- linear OOA(293, 2097150, F2, 8, 9) (dual of [(2097150, 8), 16777107, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(293, 8388601, F2, 9) (dual of [8388601, 8388508, 10]-code), using
- linear OOA(212, 65, F2, 8, 4) (dual of [(65, 8), 508, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(2105, 2097215, F2, 8, 9) (dual of [(2097215, 8), 16777615, 10]-NRT-code), using
(96, 96+9, 2796266)-Net over F2 — Digital
Digital (96, 105, 2796266)-net over F2, using
- net defined by OOA [i] based on linear OOA(2105, 2796266, F2, 9, 9) (dual of [(2796266, 9), 25166289, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2105, 2796266, F2, 8, 9) (dual of [(2796266, 8), 22370023, 10]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2105, 2796266, F2, 3, 9) (dual of [(2796266, 3), 8388693, 10]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(212, 65, F2, 3, 4) (dual of [(65, 3), 183, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 12, 65)-net over F2, using
- linear OOA(293, 2796201, F2, 3, 9) (dual of [(2796201, 3), 8388510, 10]-NRT-code), using
- OOA 3-folding [i] based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(293, large, F2, 9) (dual of [large, large−93, 10]-code), using
- linear OOA(212, 65, F2, 3, 4) (dual of [(65, 3), 183, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2105, 2796266, F2, 3, 9) (dual of [(2796266, 3), 8388693, 10]-NRT-code), using
- appending kth column [i] based on linear OOA(2105, 2796266, F2, 8, 9) (dual of [(2796266, 8), 22370023, 10]-NRT-code), using
(96, 96+9, large)-Net in Base 2 — Upper bound on s
There is no (96, 105, large)-net in base 2, because
- 7 times m-reduction [i] would yield (96, 98, large)-net in base 2, but