Best Known (204, 204+16, s)-Nets in Base 2
(204, 204+16, 1048703)-Net over F2 — Constructive and digital
Digital (204, 220, 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, 184, 1048575)-net over F2, using
- net defined by OOA [i] based on linear OOA(2184, 1048575, F2, 16, 16) (dual of [(1048575, 16), 16777016, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- net defined by OOA [i] based on linear OOA(2184, 1048575, F2, 16, 16) (dual of [(1048575, 16), 16777016, 17]-NRT-code), using
- digital (28, 36, 128)-net over F2, using
(204, 204+16, 2097406)-Net over F2 — Digital
Digital (204, 220, 2097406)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2220, 2097406, F2, 4, 16) (dual of [(2097406, 4), 8389404, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(236, 256, F2, 4, 8) (dual of [(256, 4), 988, 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(2184, 2097150, F2, 4, 16) (dual of [(2097150, 4), 8388416, 17]-NRT-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607 = 223−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- discarding factors / shortening the dual code based on linear OA(2184, large, F2, 16) (dual of [large, large−184, 17]-code), using
- OOA 4-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(236, 256, F2, 4, 8) (dual of [(256, 4), 988, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(204, 204+16, large)-Net in Base 2 — Upper bound on s
There is no (204, 220, large)-net in base 2, because
- 14 times m-reduction [i] would yield (204, 206, large)-net in base 2, but