Best Known (64, 88, s)-Nets in Base 16
(64, 88, 1542)-Net over F16 — Constructive and digital
Digital (64, 88, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (8, 16, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 8, 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, 8, 257)-net over F256, using
- digital (12, 24, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 12, 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, 12, 257)-net over F256, using
- digital (24, 48, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 24, 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, 24, 257)-net over F256, using
- digital (8, 16, 514)-net over F16, using
(64, 88, 2730)-Net in Base 16 — Constructive
(64, 88, 2730)-net in base 16, using
- net defined by OOA [i] based on OOA(1688, 2730, S16, 24, 24), using
- OA 12-folding and stacking [i] based on OA(1688, 32760, S16, 24), using
- discarding factors based on OA(1688, 32771, S16, 24), using
- discarding parts of the base [i] based on linear OA(3270, 32771, F32, 24) (dual of [32771, 32701, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(3270, 32768, F32, 24) (dual of [32768, 32698, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(3267, 32768, F32, 23) (dual of [32768, 32701, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(23) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(3270, 32771, F32, 24) (dual of [32771, 32701, 25]-code), using
- discarding factors based on OA(1688, 32771, S16, 24), using
- OA 12-folding and stacking [i] based on OA(1688, 32760, S16, 24), using
(64, 88, 25446)-Net over F16 — Digital
Digital (64, 88, 25446)-net over F16, using
(64, 88, large)-Net in Base 16 — Upper bound on s
There is no (64, 88, large)-net in base 16, because
- 22 times m-reduction [i] would yield (64, 66, large)-net in base 16, but