Best Known (72, 99, s)-Nets in Base 16
(72, 99, 1542)-Net over F16 — Constructive and digital
Digital (72, 99, 1542)-net over F16, using
- 161 times duplication [i] based on digital (71, 98, 1542)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (9, 18, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 9, 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, 9, 257)-net over F256, using
- digital (13, 26, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 13, 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, 13, 257)-net over F256, using
- digital (27, 54, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 27, 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, 27, 257)-net over F256, using
- digital (9, 18, 514)-net over F16, using
- generalized (u, u+v)-construction [i] based on
(72, 99, 2520)-Net in Base 16 — Constructive
(72, 99, 2520)-net in base 16, using
- net defined by OOA [i] based on OOA(1699, 2520, S16, 27, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(1699, 32761, S16, 27), using
- discarding factors based on OA(1699, 32771, S16, 27), using
- discarding parts of the base [i] based on linear OA(3279, 32771, F32, 27) (dual of [32771, 32692, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(25) [i] based on
- linear OA(3279, 32768, F32, 27) (dual of [32768, 32689, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(3276, 32768, F32, 26) (dual of [32768, 32692, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 32767 = 323−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(26) ⊂ Ce(25) [i] based on
- discarding parts of the base [i] based on linear OA(3279, 32771, F32, 27) (dual of [32771, 32692, 28]-code), using
- discarding factors based on OA(1699, 32771, S16, 27), using
- OOA 13-folding and stacking with additional row [i] based on OA(1699, 32761, S16, 27), using
(72, 99, 27060)-Net over F16 — Digital
Digital (72, 99, 27060)-net over F16, using
(72, 99, large)-Net in Base 16 — Upper bound on s
There is no (72, 99, large)-net in base 16, because
- 25 times m-reduction [i] would yield (72, 74, large)-net in base 16, but