Best Known (204, 221, s)-Nets in Base 2
(204, 221, 1048703)-Net over F2 — Constructive and digital
Digital (204, 221, 1048703)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (28, 36, 128)-net over F2, using
- net defined by OOA [i] based on linear OOA(236, 128, F2, 8, 8) (dual of [(128, 8), 988, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(236, 512, F2, 8) (dual of [512, 476, 9]-code), using
- 1 times truncation [i] based on linear OA(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513 | 218−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- OA 4-folding and stacking [i] based on linear OA(236, 512, F2, 8) (dual of [512, 476, 9]-code), using
- net defined by OOA [i] based on linear OOA(236, 128, F2, 8, 8) (dual of [(128, 8), 988, 9]-NRT-code), using
- digital (168, 185, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(2185, 8388601, F2, 17) (dual of [8388601, 8388416, 18]-code), using
- net defined by OOA [i] based on linear OOA(2185, 1048575, F2, 17, 17) (dual of [(1048575, 17), 17825590, 18]-NRT-code), using
- digital (28, 36, 128)-net over F2, using
(204, 221, 1677976)-Net over F2 — Digital
Digital (204, 221, 1677976)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2221, 1677976, F2, 5, 17) (dual of [(1677976, 5), 8389659, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(236, 256, F2, 5, 8) (dual of [(256, 5), 1244, 9]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 256, F2, 2, 8) (dual of [(256, 2), 476, 9]-NRT-code), using
- OOA 2-folding [i] based on linear OA(236, 512, F2, 8) (dual of [512, 476, 9]-code), using
- 1 times truncation [i] based on linear OA(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 513 | 218−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- 1 times truncation [i] based on linear OA(237, 513, F2, 9) (dual of [513, 476, 10]-code), using
- OOA 2-folding [i] based on linear OA(236, 512, F2, 8) (dual of [512, 476, 9]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(236, 256, F2, 2, 8) (dual of [(256, 2), 476, 9]-NRT-code), using
- linear OOA(2185, 1677720, F2, 5, 17) (dual of [(1677720, 5), 8388415, 18]-NRT-code), using
- OOA 5-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 8388609 | 246−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(2185, large, F2, 17) (dual of [large, large−185, 18]-code), using
- OOA 5-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- linear OOA(236, 256, F2, 5, 8) (dual of [(256, 5), 1244, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(204, 221, large)-Net in Base 2 — Upper bound on s
There is no (204, 221, large)-net in base 2, because
- 15 times m-reduction [i] would yield (204, 206, large)-net in base 2, but