Best Known (232, 247, s)-Nets in Base 2
(232, 247, 2396866)-Net over F2 — Constructive and digital
Digital (232, 247, 2396866)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (58, 65, 2097150)-net over F2, using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(265, 2097151, F2, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(265, 2097150, F2, 7, 7) (dual of [(2097150, 7), 14679985, 8]-NRT-code), using
- digital (167, 182, 1198433)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (13, 20, 62)-net over F2, using
- net defined by OOA [i] based on linear OOA(220, 62, F2, 7, 7) (dual of [(62, 7), 414, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(220, 63, F2, 3, 7) (dual of [(63, 3), 169, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(220, 62, F2, 7, 7) (dual of [(62, 7), 414, 8]-NRT-code), using
- digital (147, 162, 1198371)-net over F2, using
- net defined by OOA [i] based on linear OOA(2162, 1198371, F2, 15, 15) (dual of [(1198371, 15), 17975403, 16]-NRT-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 7-folding and stacking with additional row [i] based on linear OA(2162, 8388598, F2, 15) (dual of [8388598, 8388436, 16]-code), using
- net defined by OOA [i] based on linear OOA(2162, 1198371, F2, 15, 15) (dual of [(1198371, 15), 17975403, 16]-NRT-code), using
- digital (13, 20, 62)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (58, 65, 2097150)-net over F2, using
(232, 247, 7402689)-Net over F2 — Digital
Digital (232, 247, 7402689)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2247, 7402689, F2, 2, 15) (dual of [(7402689, 2), 14805131, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2247, large, F2, 2, 15), using
- 21 times duplication [i] based on linear OOA(2246, large, F2, 2, 15), using
- 8 times NRT-code embedding in larger space [i] based on linear OOA(2230, 8388602, F2, 2, 15) (dual of [(8388602, 2), 16776974, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(268, 4194303, F2, 2, 7) (dual of [(4194303, 2), 8388538, 8]-NRT-code), using
- linear OOA(2162, 4194301, F2, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2162, 8388602, F2, 15) (dual of [8388602, 8388440, 16]-code), using
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,14], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(2162, large, F2, 15) (dual of [large, large−162, 16]-code), using
- OOA 2-folding [i] based on linear OA(2162, 8388602, F2, 15) (dual of [8388602, 8388440, 16]-code), using
- (u, u+v)-construction [i] based on
- 8 times NRT-code embedding in larger space [i] based on linear OOA(2230, 8388602, F2, 2, 15) (dual of [(8388602, 2), 16776974, 16]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2246, large, F2, 2, 15), using
- discarding factors / shortening the dual code based on linear OOA(2247, large, F2, 2, 15), using
(232, 247, large)-Net in Base 2 — Upper bound on s
There is no (232, 247, large)-net in base 2, because
- 13 times m-reduction [i] would yield (232, 234, large)-net in base 2, but