Best Known (177, 177+17, s)-Nets in Base 2
(177, 177+17, 1048580)-Net over F2 — Constructive and digital
Digital (177, 194, 1048580)-net over F2, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 5)-net over F2, using
- net from sequence [i] based on digital (1, 4)-sequence over F2, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- Niederreiter–Xing sequence (Piršić implementation) with equidistant coordinate [i]
- net from sequence [i] based on digital (1, 4)-sequence over F2, 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 (1, 9, 5)-net over F2, using
(177, 177+17, 1398105)-Net over F2 — Digital
Digital (177, 194, 1398105)-net over F2, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2194, 1398105, F2, 6, 17) (dual of [(1398105, 6), 8388436, 18]-NRT-code), using
- (u, u+v)-construction [i] based on
- linear OOA(29, 5, F2, 6, 8) (dual of [(5, 6), 21, 9]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(6;F,21P) [i] based on function field F/F2 with g(F) = 1 and N(F) ≥ 5, using
- linear OOA(2185, 1398100, F2, 6, 17) (dual of [(1398100, 6), 8388415, 18]-NRT-code), using
- OOA 6-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 6-folding [i] based on linear OA(2185, 8388600, F2, 17) (dual of [8388600, 8388415, 18]-code), using
- linear OOA(29, 5, F2, 6, 8) (dual of [(5, 6), 21, 9]-NRT-code), using
- (u, u+v)-construction [i] based on
(177, 177+17, large)-Net in Base 2 — Upper bound on s
There is no (177, 194, large)-net in base 2, because
- 15 times m-reduction [i] would yield (177, 179, large)-net in base 2, but