Best Known (178, 178+15, s)-Nets in Base 2
(178, 178+15, 1198881)-Net over F2 — Constructive and digital
Digital (178, 193, 1198881)-net over F2, using
- 22 times duplication [i] based on digital (176, 191, 1198881)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (22, 29, 510)-net over F2, using
- net defined by OOA [i] based on linear OOA(229, 510, F2, 7, 7) (dual of [(510, 7), 3541, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(229, 511, F2, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(229, 510, F2, 7, 7) (dual of [(510, 7), 3541, 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 (22, 29, 510)-net over F2, using
- (u, u+v)-construction [i] based on
(178, 178+15, 2097662)-Net over F2 — Digital
Digital (178, 193, 2097662)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2193, 2097662, F2, 4, 15) (dual of [(2097662, 4), 8390455, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(229, 511, F2, 4, 7) (dual of [(511, 4), 2015, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(229, 511, F2, 3, 7) (dual of [(511, 3), 1504, 8]-NRT-code), using
- linear OOA(2164, 2097151, F2, 4, 15) (dual of [(2097151, 4), 8388440, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2164, 4194302, F2, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on 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
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2162, 4194301, F2, 2, 15) (dual of [(4194301, 2), 8388440, 16]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2164, 4194302, F2, 2, 15) (dual of [(4194302, 2), 8388440, 16]-NRT-code), using
- linear OOA(229, 511, F2, 4, 7) (dual of [(511, 4), 2015, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
(178, 178+15, large)-Net in Base 2 — Upper bound on s
There is no (178, 193, large)-net in base 2, because
- 13 times m-reduction [i] would yield (178, 180, large)-net in base 2, but