Best Known (61, 61+23, s)-Nets in Base 16
(61, 61+23, 1544)-Net over F16 — Constructive and digital
Digital (61, 84, 1544)-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 (25, 48, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 24, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 24, 258)-net over F256, using
- digital (7, 14, 514)-net over F16, using
(61, 61+23, 2979)-Net in Base 16 — Constructive
(61, 84, 2979)-net in base 16, using
- net defined by OOA [i] based on OOA(1684, 2979, S16, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(1684, 32770, S16, 23), using
- discarding factors based on OA(1684, 32771, S16, 23), using
- discarding parts of the base [i] based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(21) [i] based on
- 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(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(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(22) ⊂ Ce(21) [i] based on
- discarding parts of the base [i] based on linear OA(3267, 32771, F32, 23) (dual of [32771, 32704, 24]-code), using
- discarding factors based on OA(1684, 32771, S16, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(1684, 32770, S16, 23), using
(61, 61+23, 23906)-Net over F16 — Digital
Digital (61, 84, 23906)-net over F16, using
(61, 61+23, large)-Net in Base 16 — Upper bound on s
There is no (61, 84, large)-net in base 16, because
- 21 times m-reduction [i] would yield (61, 63, large)-net in base 16, but