Best Known (159, 159+14, s)-Nets in Base 2
(159, 159+14, 1198384)-Net over F2 — Constructive and digital
Digital (159, 173, 1198384)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (5, 12, 13)-net over F2, 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
(159, 159+14, 1863901)-Net over F2 — Digital
Digital (159, 173, 1863901)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2173, 1863901, F2, 4, 14) (dual of [(1863901, 4), 7455431, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2173, 2097157, F2, 4, 14) (dual of [(2097157, 4), 8388455, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2173, 4194314, F2, 2, 14) (dual of [(4194314, 2), 8388455, 15]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(212, 13, F2, 2, 7) (dual of [(13, 2), 14, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (5, 12, 13)-net over F2, using
- linear OOA(2161, 4194301, F2, 2, 14) (dual of [(4194301, 2), 8388441, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2161, 8388602, F2, 14) (dual of [8388602, 8388441, 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
- OOA 2-folding [i] based on linear OA(2161, 8388602, F2, 14) (dual of [8388602, 8388441, 15]-code), using
- linear OOA(212, 13, F2, 2, 7) (dual of [(13, 2), 14, 8]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA 2-folding [i] based on linear OOA(2173, 4194314, F2, 2, 14) (dual of [(4194314, 2), 8388455, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2173, 2097157, F2, 4, 14) (dual of [(2097157, 4), 8388455, 15]-NRT-code), using
(159, 159+14, large)-Net in Base 2 — Upper bound on s
There is no (159, 173, large)-net in base 2, because
- 12 times m-reduction [i] would yield (159, 161, large)-net in base 2, but