Best Known (84, 102, s)-Nets in Base 32
(84, 102, 932166)-Net over F32 — Constructive and digital
Digital (84, 102, 932166)-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 (68, 86, 932067)-net over F32, using
- net defined by OOA [i] based on linear OOA(3286, 932067, F32, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(3286, large, F32, 18) (dual of [large, large−86, 19]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OA 9-folding and stacking [i] based on linear OA(3286, large, F32, 18) (dual of [large, large−86, 19]-code), using
- net defined by OOA [i] based on linear OOA(3286, 932067, F32, 18, 18) (dual of [(932067, 18), 16777120, 19]-NRT-code), using
- digital (7, 16, 99)-net over F32, using
(84, 102, 932389)-Net in Base 32 — Constructive
(84, 102, 932389)-net in base 32, using
- base change [i] based on (67, 85, 932389)-net in base 64, using
- (u, u+v)-construction [i] based on
- (7, 16, 322)-net in base 64, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 65)-net over F64, using
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 0 and N(F) ≥ 65, using
- the rational function field F64(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 64)-sequence over F64, using
- (3, 12, 257)-net in base 64, using
- base change [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
- base change [i] based on digital (0, 9, 257)-net over F256, using
- digital (0, 4, 65)-net over F64, using
- (u, u+v)-construction [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
- (7, 16, 322)-net in base 64, using
- (u, u+v)-construction [i] based on
(84, 102, large)-Net over F32 — Digital
Digital (84, 102, large)-net over F32, using
- t-expansion [i] based on digital (83, 102, large)-net over F32, using
- 3 times m-reduction [i] based on digital (83, 105, large)-net over F32, using
(84, 102, large)-Net in Base 32 — Upper bound on s
There is no (84, 102, large)-net in base 32, because
- 16 times m-reduction [i] would yield (84, 86, large)-net in base 32, but