Best Known (260−15, 260, s)-Nets in Base 2
(260−15, 260, 2398786)-Net over F2 — Constructive and digital
Digital (245, 260, 2398786)-net over F2, using
- 21 times duplication [i] based on digital (244, 259, 2398786)-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 (179, 194, 1199393)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (25, 32, 1022)-net over F2, using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(232, 1023, F2, 3, 7) (dual of [(1023, 3), 3037, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(232, 1022, F2, 7, 7) (dual of [(1022, 7), 7122, 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 (25, 32, 1022)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (58, 65, 2097150)-net over F2, using
- (u, u+v)-construction [i] based on
(260−15, 260, large)-Net over F2 — Digital
Digital (245, 260, large)-net over F2, using
- 210 times duplication [i] based on digital (235, 250, large)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2250, large, F2, 2, 15), using
- 10 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
- 10 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
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2250, large, F2, 2, 15), using
(260−15, 260, large)-Net in Base 2 — Upper bound on s
There is no (245, 260, large)-net in base 2, because
- 13 times m-reduction [i] would yield (245, 247, large)-net in base 2, but