Best Known (25, 25+17, s)-Nets in Base 256
(25, 25+17, 8450)-Net over F256 — Constructive and digital
Digital (25, 42, 8450)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (16, 33, 8192)-net over F256, using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(25633, 65537, F256, 17) (dual of [65537, 65504, 18]-code), using
- net defined by OOA [i] based on linear OOA(25633, 8192, F256, 17, 17) (dual of [(8192, 17), 139231, 18]-NRT-code), using
- digital (1, 9, 258)-net over F256, using
(25, 25+17, 65827)-Net over F256 — Digital
Digital (25, 42, 65827)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25642, 65827, F256, 17) (dual of [65827, 65785, 18]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2569, 289, F256, 8) (dual of [289, 280, 9]-code), using
- extended algebraic-geometric code AGe(F,280P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- linear OA(25633, 65538, F256, 17) (dual of [65538, 65505, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(25633, 65536, F256, 17) (dual of [65536, 65503, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(25631, 65536, F256, 16) (dual of [65536, 65505, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(2560, 2, F256, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(2560, s, F256, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(2569, 289, F256, 8) (dual of [289, 280, 9]-code), using
- (u, u+v)-construction [i] based on
(25, 25+17, large)-Net in Base 256 — Upper bound on s
There is no (25, 42, large)-net in base 256, because
- 15 times m-reduction [i] would yield (25, 27, large)-net in base 256, but