Best Known (53−19, 53, s)-Nets in Base 32
(53−19, 53, 396)-Net over F32 — Constructive and digital
Digital (34, 53, 396)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 1, 33)-net over F32, using
- s-reduction based on digital (0, 1, s)-net over F32 with arbitrarily large s, using
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 1, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32, using
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 2, 33)-net over F32 (see above)
- digital (0, 3, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 0 and N(F) ≥ 33, using
- the rational function field F32(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 32)-sequence over F32, using
- digital (0, 3, 33)-net over F32 (see above)
- digital (0, 4, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 6, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 9, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 19, 33)-net over F32, using
- net from sequence [i] based on digital (0, 32)-sequence over F32 (see above)
- digital (0, 1, 33)-net over F32, using
(53−19, 53, 1820)-Net in Base 32 — Constructive
(34, 53, 1820)-net in base 32, using
- 321 times duplication [i] based on (33, 52, 1820)-net in base 32, using
- net defined by OOA [i] based on OOA(3252, 1820, S32, 19, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(3252, 16381, S32, 19), using
- discarding factors based on OA(3252, 16386, S32, 19), using
- discarding parts of the base [i] based on linear OA(12837, 16386, F128, 19) (dual of [16386, 16349, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- linear OA(12837, 16384, F128, 19) (dual of [16384, 16347, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(12835, 16384, F128, 18) (dual of [16384, 16349, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(1280, 2, F128, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(18) ⊂ Ce(17) [i] based on
- discarding parts of the base [i] based on linear OA(12837, 16386, F128, 19) (dual of [16386, 16349, 20]-code), using
- discarding factors based on OA(3252, 16386, S32, 19), using
- OOA 9-folding and stacking with additional row [i] based on OA(3252, 16381, S32, 19), using
- net defined by OOA [i] based on OOA(3252, 1820, S32, 19, 19), using
(53−19, 53, 6595)-Net over F32 — Digital
Digital (34, 53, 6595)-net over F32, using
(53−19, 53, large)-Net in Base 32 — Upper bound on s
There is no (34, 53, large)-net in base 32, because
- 17 times m-reduction [i] would yield (34, 36, large)-net in base 32, but