Best Known (199−14, 199, s)-Nets in Base 2
(199−14, 199, 1202465)-Net over F2 — Constructive and digital
Digital (185, 199, 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, 161, 1198371)-net over F2, using
- net defined by OOA [i] based on linear OOA(2161, 1198371, F2, 14, 14) (dual of [(1198371, 14), 16777033, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(2161, 8388597, F2, 14) (dual of [8388597, 8388436, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(2161, 8388597, F2, 14) (dual of [8388597, 8388436, 15]-code), using
- net defined by OOA [i] based on linear OOA(2161, 1198371, F2, 14, 14) (dual of [(1198371, 14), 16777033, 15]-NRT-code), using
- digital (31, 38, 4094)-net over F2, using
(199−14, 199, 2800296)-Net over F2 — Digital
Digital (185, 199, 2800296)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2199, 2800296, F2, 3, 14) (dual of [(2800296, 3), 8400689, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(238, 4095, F2, 3, 7) (dual of [(4095, 3), 12247, 8]-NRT-code), using
- linear OOA(2161, 2796201, F2, 3, 14) (dual of [(2796201, 3), 8388442, 15]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- OOA 3-folding [i] based on linear OA(2161, large, F2, 14) (dual of [large, large−161, 15]-code), using
- (u, u+v)-construction [i] based on
(199−14, 199, large)-Net in Base 2 — Upper bound on s
There is no (185, 199, large)-net in base 2, because
- 12 times m-reduction [i] would yield (185, 187, large)-net in base 2, but