Best Known (213−19, 213, s)-Nets in Base 2
(213−19, 213, 932067)-Net over F2 — Constructive and digital
Digital (194, 213, 932067)-net over F2, using
- 22 times duplication [i] based on digital (192, 211, 932067)-net over F2, using
- net defined by OOA [i] based on linear OOA(2211, 932067, F2, 21, 19) (dual of [(932067, 21), 19573196, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2211, 2796202, F2, 3, 19) (dual of [(2796202, 3), 8388395, 20]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- OOA 3-folding [i] based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2208, 2796201, F2, 3, 19) (dual of [(2796201, 3), 8388395, 20]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OOA(2211, 2796202, F2, 3, 19) (dual of [(2796202, 3), 8388395, 20]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2211, 932067, F2, 21, 19) (dual of [(932067, 21), 19573196, 20]-NRT-code), using
(213−19, 213, 1198371)-Net over F2 — Digital
Digital (194, 213, 1198371)-net over F2, using
- 25 times duplication [i] based on digital (189, 208, 1198371)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2208, 1198371, F2, 7, 19) (dual of [(1198371, 7), 8388389, 20]-NRT-code), using
- OOA 7-folding [i] based on linear OA(2208, 8388597, F2, 19) (dual of [8388597, 8388389, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2208, large, F2, 19) (dual of [large, large−208, 20]-code), using
- OOA 7-folding [i] based on linear OA(2208, 8388597, F2, 19) (dual of [8388597, 8388389, 20]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2208, 1198371, F2, 7, 19) (dual of [(1198371, 7), 8388389, 20]-NRT-code), using
(213−19, 213, large)-Net in Base 2 — Upper bound on s
There is no (194, 213, large)-net in base 2, because
- 17 times m-reduction [i] would yield (194, 196, large)-net in base 2, but