Best Known (96−8, 96, s)-Nets in Base 2
(96−8, 96, 2097153)-Net over F2 — Constructive and digital
Digital (88, 96, 2097153)-net over F2, using
- net defined by OOA [i] based on linear OOA(296, 2097153, F2, 8, 8) (dual of [(2097153, 8), 16777128, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(296, 2097153, F2, 7, 8) (dual of [(2097153, 7), 14679975, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(24, 3, F2, 7, 4) (dual of [(3, 7), 17, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(7;17,2) [i]
- linear OOA(292, 2097150, F2, 7, 8) (dual of [(2097150, 7), 14679958, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(292, 8388600, F2, 8) (dual of [8388600, 8388508, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- discarding factors / shortening the dual code based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(292, 8388600, F2, 8) (dual of [8388600, 8388508, 9]-code), using
- linear OOA(24, 3, F2, 7, 4) (dual of [(3, 7), 17, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- appending kth column [i] based on linear OOA(296, 2097153, F2, 7, 8) (dual of [(2097153, 7), 14679975, 9]-NRT-code), using
(96−8, 96, 2796204)-Net over F2 — Digital
Digital (88, 96, 2796204)-net over F2, using
- net defined by OOA [i] based on linear OOA(296, 2796204, F2, 8, 8) (dual of [(2796204, 8), 22369536, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(296, 2796204, F2, 7, 8) (dual of [(2796204, 7), 19573332, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(296, 2796204, F2, 3, 8) (dual of [(2796204, 3), 8388516, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(24, 3, F2, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- extended Reed–Solomon NRT-code RSe(3;5,2) [i]
- linear OOA(292, 2796201, F2, 3, 8) (dual of [(2796201, 3), 8388511, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- OOA 3-folding [i] based on linear OA(292, large, F2, 8) (dual of [large, large−92, 9]-code), using
- linear OOA(24, 3, F2, 3, 4) (dual of [(3, 3), 5, 5]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(296, 2796204, F2, 3, 8) (dual of [(2796204, 3), 8388516, 9]-NRT-code), using
- appending kth column [i] based on linear OOA(296, 2796204, F2, 7, 8) (dual of [(2796204, 7), 19573332, 9]-NRT-code), using
(96−8, 96, large)-Net in Base 2 — Upper bound on s
There is no (88, 96, large)-net in base 2, because
- 6 times m-reduction [i] would yield (88, 90, large)-net in base 2, but