Best Known (67, 85, s)-Nets in Base 32
(67, 85, 116607)-Net over F32 — Constructive and digital
Digital (67, 85, 116607)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 16, 99)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- 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, 4, 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, 3, 33)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (51, 69, 116508)-net over F32, using
- net defined by OOA [i] based on linear OOA(3269, 116508, F32, 18, 18) (dual of [(116508, 18), 2097075, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3269, 1048572, F32, 18) (dual of [1048572, 1048503, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using
- an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- discarding factors / shortening the dual code based on linear OA(3269, 1048576, F32, 18) (dual of [1048576, 1048507, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(3269, 1048572, F32, 18) (dual of [1048572, 1048503, 19]-code), using
- net defined by OOA [i] based on linear OOA(3269, 116508, F32, 18, 18) (dual of [(116508, 18), 2097075, 19]-NRT-code), using
- digital (7, 16, 99)-net over F32, using
(67, 85, 932067)-Net in Base 32 — Constructive
(67, 85, 932067)-net in base 32, using
- 321 times duplication [i] based on (66, 84, 932067)-net in base 32, using
- base change [i] based on digital (52, 70, 932067)-net over F64, using
- 641 times duplication [i] based on digital (51, 69, 932067)-net over F64, using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- net defined by OOA [i] based on linear OOA(6469, 932067, F64, 18, 18) (dual of [(932067, 18), 16777137, 19]-NRT-code), using
- 641 times duplication [i] based on digital (51, 69, 932067)-net over F64, using
- base change [i] based on digital (52, 70, 932067)-net over F64, using
(67, 85, 7768441)-Net over F32 — Digital
Digital (67, 85, 7768441)-net over F32, using
(67, 85, large)-Net in Base 32 — Upper bound on s
There is no (67, 85, large)-net in base 32, because
- 16 times m-reduction [i] would yield (67, 69, large)-net in base 32, but