Best Known (211−18, 211, s)-Nets in Base 2
(211−18, 211, 932067)-Net over F2 — Constructive and digital
Digital (193, 211, 932067)-net over F2, using
- t-expansion [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
(211−18, 211, 1398101)-Net over F2 — Digital
Digital (193, 211, 1398101)-net over F2, using
- 21 times duplication [i] based on digital (192, 210, 1398101)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2210, 1398101, F2, 6, 18) (dual of [(1398101, 6), 8388396, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2210, 2796202, F2, 3, 18) (dual of [(2796202, 3), 8388396, 19]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2207, 2796201, F2, 3, 18) (dual of [(2796201, 3), 8388396, 19]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 3-folding [i] based on linear OA(2207, large, F2, 18) (dual of [large, large−207, 19]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2207, 2796201, F2, 3, 18) (dual of [(2796201, 3), 8388396, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2210, 2796202, F2, 3, 18) (dual of [(2796202, 3), 8388396, 19]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2210, 1398101, F2, 6, 18) (dual of [(1398101, 6), 8388396, 19]-NRT-code), using
(211−18, 211, large)-Net in Base 2 — Upper bound on s
There is no (193, 211, large)-net in base 2, because
- 16 times m-reduction [i] would yield (193, 195, large)-net in base 2, but