Best Known (236, 253, s)-Nets in Base 2
(236, 253, 1081343)-Net over F2 — Constructive and digital
Digital (236, 253, 1081343)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (60, 68, 32768)-net over F2, using
- net defined by OOA [i] based on linear OOA(268, 32768, F2, 8, 8) (dual of [(32768, 8), 262076, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(268, 131072, F2, 8) (dual of [131072, 131004, 9]-code), using
- 1 times truncation [i] based on linear OA(269, 131073, F2, 9) (dual of [131073, 131004, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(269, 131073, F2, 9) (dual of [131073, 131004, 10]-code), using
- OA 4-folding and stacking [i] based on linear OA(268, 131072, F2, 8) (dual of [131072, 131004, 9]-code), using
- net defined by OOA [i] based on linear OOA(268, 32768, F2, 8, 8) (dual of [(32768, 8), 262076, 9]-NRT-code), using
- digital (168, 185, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- digital (60, 68, 32768)-net over F2, using
(236, 253, 2839891)-Net over F2 — Digital
Digital (236, 253, 2839891)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2253, 2839891, F2, 3, 17) (dual of [(2839891, 3), 8519420, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(268, 43690, F2, 3, 8) (dual of [(43690, 3), 131002, 9]-NRT-code), using
- OOA 3-folding [i] based on linear OA(268, 131070, F2, 8) (dual of [131070, 131002, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(268, 131072, F2, 8) (dual of [131072, 131004, 9]-code), using
- 1 times truncation [i] based on linear OA(269, 131073, F2, 9) (dual of [131073, 131004, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 131073 | 234−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(269, 131073, F2, 9) (dual of [131073, 131004, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(268, 131072, F2, 8) (dual of [131072, 131004, 9]-code), using
- OOA 3-folding [i] based on linear OA(268, 131070, F2, 8) (dual of [131070, 131002, 9]-code), using
- linear OOA(2185, 2796201, F2, 3, 17) (dual of [(2796201, 3), 8388418, 18]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- linear OOA(268, 43690, F2, 3, 8) (dual of [(43690, 3), 131002, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(236, 253, large)-Net in Base 2 — Upper bound on s
There is no (236, 253, large)-net in base 2, because
- 15 times m-reduction [i] would yield (236, 238, large)-net in base 2, but