Best Known (194, 194+12, s)-Nets in Base 2
(194, 194+12, 2796201)-Net over F2 — Constructive and digital
Digital (194, 206, 2796201)-net over F2, using
- t-expansion [i] based on digital (193, 206, 2796201)-net over F2, using
- net defined by OOA [i] based on linear OOA(2206, 2796201, F2, 18, 13) (dual of [(2796201, 18), 50331412, 14]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(2206, 2796202, F2, 6, 13) (dual of [(2796202, 6), 16777006, 14]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(264, 2097149, F2, 6, 6) (dual of [(2097149, 6), 12582830, 7]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(264, 2097150, F2, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
- 1 step truncation [i] based on linear OOA(265, 2097151, F2, 3, 7) (dual of [(2097151, 3), 6291388, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(264, 2097150, F2, 3, 6) (dual of [(2097150, 3), 6291386, 7]-NRT-code), using
- linear OOA(2142, 1398101, F2, 6, 13) (dual of [(1398101, 6), 8388464, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2142, 2796202, F2, 3, 13) (dual of [(2796202, 3), 8388464, 14]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2139, 2796201, F2, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
- OOA 3-folding [i] based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,6], and minimum distance d ≥ |{−6,−5,…,6}|+1 = 14 (BCH-bound) [i]
- OOA 3-folding [i] based on linear OA(2139, large, F2, 13) (dual of [large, large−139, 14]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2139, 2796201, F2, 3, 13) (dual of [(2796201, 3), 8388464, 14]-NRT-code), using
- OOA 2-folding [i] based on linear OOA(2142, 2796202, F2, 3, 13) (dual of [(2796202, 3), 8388464, 14]-NRT-code), using
- linear OOA(264, 2097149, F2, 6, 6) (dual of [(2097149, 6), 12582830, 7]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(2206, 2796202, F2, 6, 13) (dual of [(2796202, 6), 16777006, 14]-NRT-code), using
- net defined by OOA [i] based on linear OOA(2206, 2796201, F2, 18, 13) (dual of [(2796201, 18), 50331412, 14]-NRT-code), using
(194, 194+12, 8388602)-Net over F2 — Digital
Digital (194, 206, 8388602)-net over F2, using
- 21 times duplication [i] based on digital (193, 205, 8388602)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2205, 8388602, F2, 2, 12) (dual of [(8388602, 2), 16776999, 13]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(267, 4194303, F2, 2, 6) (dual of [(4194303, 2), 8388539, 7]-NRT-code), using
- linear OOA(2138, 4194301, F2, 2, 12) (dual of [(4194301, 2), 8388464, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- discarding factors / shortening the dual code based on linear OA(2138, large, F2, 12) (dual of [large, large−138, 13]-code), using
- OOA 2-folding [i] based on linear OA(2138, 8388602, F2, 12) (dual of [8388602, 8388464, 13]-code), using
- (u, u+v)-construction [i] based on
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2205, 8388602, F2, 2, 12) (dual of [(8388602, 2), 16776999, 13]-NRT-code), using
(194, 194+12, large)-Net in Base 2 — Upper bound on s
There is no (194, 206, large)-net in base 2, because
- 10 times m-reduction [i] would yield (194, 196, large)-net in base 2, but