Best Known (58, 58+22, s)-Nets in Base 16
(58, 58+22, 1542)-Net over F16 — Constructive and digital
Digital (58, 80, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 14, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 7, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 7, 257)-net over F256, using
- digital (11, 22, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 11, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 11, 257)-net over F256, using
- digital (22, 44, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 22, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256 (see above)
- trace code for nets [i] based on digital (0, 22, 257)-net over F256, using
- digital (7, 14, 514)-net over F16, using
(58, 58+22, 2979)-Net in Base 16 — Constructive
(58, 80, 2979)-net in base 16, using
- base change [i] based on digital (42, 64, 2979)-net over F32, using
- net defined by OOA [i] based on linear OOA(3264, 2979, F32, 22, 22) (dual of [(2979, 22), 65474, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(3264, 32769, F32, 22) (dual of [32769, 32705, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3264, 32771, F32, 22) (dual of [32771, 32707, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- linear OA(3264, 32768, F32, 22) (dual of [32768, 32704, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(3261, 32768, F32, 21) (dual of [32768, 32707, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(320, 3, F32, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(3264, 32771, F32, 22) (dual of [32771, 32707, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(3264, 32769, F32, 22) (dual of [32769, 32705, 23]-code), using
- net defined by OOA [i] based on linear OOA(3264, 2979, F32, 22, 22) (dual of [(2979, 22), 65474, 23]-NRT-code), using
(58, 58+22, 22373)-Net over F16 — Digital
Digital (58, 80, 22373)-net over F16, using
(58, 58+22, large)-Net in Base 16 — Upper bound on s
There is no (58, 80, large)-net in base 16, because
- 20 times m-reduction [i] would yield (58, 60, large)-net in base 16, but