Best Known (58−24, 58, s)-Nets in Base 32
(58−24, 58, 240)-Net over F32 — Constructive and digital
Digital (34, 58, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 23, 171)-net over F32, using
- net defined by OOA [i] based on linear OOA(3223, 171, F32, 12, 12) (dual of [(171, 12), 2029, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
- construction X applied to Ce(11) ⊂ Ce(10) [i] based on
- linear OA(3223, 1024, F32, 12) (dual of [1024, 1001, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(3221, 1024, F32, 11) (dual of [1024, 1003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 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(11) ⊂ Ce(10) [i] based on
- OA 6-folding and stacking [i] based on linear OA(3223, 1026, F32, 12) (dual of [1026, 1003, 13]-code), using
- net defined by OOA [i] based on linear OOA(3223, 171, F32, 12, 12) (dual of [(171, 12), 2029, 13]-NRT-code), using
- digital (11, 35, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (11, 23, 171)-net over F32, using
(58−24, 58, 407)-Net in Base 32 — Constructive
(34, 58, 407)-net in base 32, using
- (u, u+v)-construction [i] based on
- (7, 19, 150)-net in base 32, using
- 2 times m-reduction [i] based on (7, 21, 150)-net in base 32, using
- base change [i] based on digital (1, 15, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- base change [i] based on digital (1, 15, 150)-net over F128, using
- 2 times m-reduction [i] based on (7, 21, 150)-net in base 32, using
- (15, 39, 257)-net in base 32, using
- 1 times m-reduction [i] based on (15, 40, 257)-net in base 32, using
- base change [i] based on digital (0, 25, 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
- base change [i] based on digital (0, 25, 257)-net over F256, using
- 1 times m-reduction [i] based on (15, 40, 257)-net in base 32, using
- (7, 19, 150)-net in base 32, using
(58−24, 58, 1911)-Net over F32 — Digital
Digital (34, 58, 1911)-net over F32, using
(58−24, 58, 3212850)-Net in Base 32 — Upper bound on s
There is no (34, 58, 3212851)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 1989 298394 449608 856859 177994 080769 304812 995539 945305 250672 422996 750897 936556 341852 307356 > 3258 [i]