Best Known (13, 22, s)-Nets in Base 256
(13, 22, 16642)-Net over F256 — Constructive and digital
Digital (13, 22, 16642)-net over F256, using
- (u, u+v)-construction [i] based on
- digital (1, 5, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- digital (8, 17, 16384)-net over F256, using
- net defined by OOA [i] based on linear OOA(25617, 16384, F256, 9, 9) (dual of [(16384, 9), 147439, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- OOA 4-folding and stacking with additional row [i] based on linear OA(25617, 65537, F256, 9) (dual of [65537, 65520, 10]-code), using
- net defined by OOA [i] based on linear OOA(25617, 16384, F256, 9, 9) (dual of [(16384, 9), 147439, 10]-NRT-code), using
- digital (1, 5, 258)-net over F256, using
(13, 22, 65827)-Net over F256 — Digital
Digital (13, 22, 65827)-net over F256, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(25622, 65827, F256, 9) (dual of [65827, 65805, 10]-code), using
- (u, u+v)-construction [i] based on
- linear OA(2565, 289, F256, 4) (dual of [289, 284, 5]-code), using
- extended algebraic-geometric code AGe(F,284P) [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- linear OA(25617, 65538, F256, 9) (dual of [65538, 65521, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(7) [i] based on
- linear OA(25617, 65536, F256, 9) (dual of [65536, 65519, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(25615, 65536, F256, 8) (dual of [65536, 65521, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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(8) ⊂ Ce(7) [i] based on
- linear OA(2565, 289, F256, 4) (dual of [289, 284, 5]-code), using
- (u, u+v)-construction [i] based on
(13, 22, large)-Net in Base 256 — Upper bound on s
There is no (13, 22, large)-net in base 256, because
- 7 times m-reduction [i] would yield (13, 15, large)-net in base 256, but