Best Known (174, 174+15, s)-Nets in Base 2
(174, 174+15, 1198625)-Net over F2 — Constructive and digital
Digital (174, 189, 1198625)-net over F2, using
- 21 times duplication [i] based on digital (173, 188, 1198625)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (19, 26, 254)-net over F2, using
- net defined by OOA [i] based on linear OOA(226, 254, F2, 7, 7) (dual of [(254, 7), 1752, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(226, 255, F2, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(226, 254, F2, 7, 7) (dual of [(254, 7), 1752, 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 (19, 26, 254)-net over F2, using
- (u, u+v)-construction [i] based on
(174, 174+15, 1678911)-Net over F2 — Digital
Digital (174, 189, 1678911)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2189, 1678911, F2, 4, 15) (dual of [(1678911, 4), 6715455, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2189, 2097404, F2, 4, 15) (dual of [(2097404, 4), 8389427, 16]-NRT-code), using
- 21 times duplication [i] based on linear OOA(2188, 2097404, F2, 4, 15) (dual of [(2097404, 4), 8389428, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(226, 254, F2, 4, 7) (dual of [(254, 4), 990, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(226, 255, F2, 3, 7) (dual of [(255, 3), 739, 8]-NRT-code), using
- linear OOA(2162, 2097150, F2, 4, 15) (dual of [(2097150, 4), 8388438, 16]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 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 4-folding [i] based on linear OA(2162, 8388600, F2, 15) (dual of [8388600, 8388438, 16]-code), using
- linear OOA(226, 254, F2, 4, 7) (dual of [(254, 4), 990, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- 21 times duplication [i] based on linear OOA(2188, 2097404, F2, 4, 15) (dual of [(2097404, 4), 8389428, 16]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2189, 2097404, F2, 4, 15) (dual of [(2097404, 4), 8389427, 16]-NRT-code), using
(174, 174+15, large)-Net in Base 2 — Upper bound on s
There is no (174, 189, large)-net in base 2, because
- 13 times m-reduction [i] would yield (174, 176, large)-net in base 2, but