Best Known (186, 186+15, s)-Nets in Base 2
(186, 186+15, 1202465)-Net over F2 — Constructive and digital
Digital (186, 201, 1202465)-net over F2, using
- 21 times duplication [i] based on digital (185, 200, 1202465)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (31, 38, 4094)-net over F2, using
- net defined by OOA [i] based on linear OOA(238, 4094, F2, 7, 7) (dual of [(4094, 7), 28620, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(238, 4095, F2, 3, 7) (dual of [(4095, 3), 12247, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(238, 4094, F2, 7, 7) (dual of [(4094, 7), 28620, 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 (31, 38, 4094)-net over F2, using
- (u, u+v)-construction [i] based on
(186, 186+15, 2101245)-Net over F2 — Digital
Digital (186, 201, 2101245)-net over F2, using
- 21 times duplication [i] based on digital (185, 200, 2101245)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2200, 2101245, F2, 4, 15) (dual of [(2101245, 4), 8404780, 16]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(238, 4095, F2, 4, 7) (dual of [(4095, 4), 16342, 8]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(238, 4095, F2, 3, 7) (dual of [(4095, 3), 12247, 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(238, 4095, F2, 4, 7) (dual of [(4095, 4), 16342, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2200, 2101245, F2, 4, 15) (dual of [(2101245, 4), 8404780, 16]-NRT-code), using
(186, 186+15, large)-Net in Base 2 — Upper bound on s
There is no (186, 201, large)-net in base 2, because
- 13 times m-reduction [i] would yield (186, 188, large)-net in base 2, but