Best Known (179, 195, s)-Nets in Base 2
(179, 195, 1048582)-Net over F2 — Constructive and digital
Digital (179, 195, 1048582)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 7)-net over F2, using
- net from sequence [i] based on digital (3, 6)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (3, 6)-sequence over F2, 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 (3, 11, 7)-net over F2, using
(179, 195, 1677727)-Net over F2 — Digital
Digital (179, 195, 1677727)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2195, 1677727, F2, 5, 16) (dual of [(1677727, 5), 8388440, 17]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(211, 7, F2, 5, 8) (dual of [(7, 5), 24, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(5;F,26P) [i] based on function field F/F2 with g(F) = 3 and N(F) ≥ 7, using
- linear OOA(2184, 1677720, F2, 5, 16) (dual of [(1677720, 5), 8388416, 17]-NRT-code), using
- OOA 5-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 5-folding [i] based on linear OA(2184, 8388600, F2, 16) (dual of [8388600, 8388416, 17]-code), using
- linear OOA(211, 7, F2, 5, 8) (dual of [(7, 5), 24, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(179, 195, large)-Net in Base 2 — Upper bound on s
There is no (179, 195, large)-net in base 2, because
- 14 times m-reduction [i] would yield (179, 181, large)-net in base 2, but