Best Known (82, 82+18, s)-Nets in Base 32
(82, 82+18, 932144)-Net over F32 — Constructive and digital
Digital (82, 100, 932144)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 14, 77)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 4, 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 (1, 10, 44)-net over F32, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 1 and N(F) ≥ 44, using
- net from sequence [i] based on digital (1, 43)-sequence over F32, using
- digital (0, 4, 33)-net over F32, using
- (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 (5, 14, 77)-net over F32, using
(82, 82+18, 932325)-Net in Base 32 — Constructive
(82, 100, 932325)-net in base 32, using
- 321 times duplication [i] based on (81, 99, 932325)-net in base 32, using
- (u, u+v)-construction [i] based on
- (7, 16, 258)-net in base 32, using
- base change [i] based on digital (1, 10, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 10, 258)-net over F256, using
- (65, 83, 932067)-net in base 32, using
- net defined by OOA [i] based on OOA(3283, 932067, S32, 18, 18), using
- OA 9-folding and stacking [i] based on OA(3283, large, S32, 18), using
- discarding parts of the base [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]
- discarding parts of the base [i] based on linear OA(6469, large, F64, 18) (dual of [large, large−69, 19]-code), using
- OA 9-folding and stacking [i] based on OA(3283, large, S32, 18), using
- net defined by OOA [i] based on OOA(3283, 932067, S32, 18, 18), using
- (7, 16, 258)-net in base 32, using
- (u, u+v)-construction [i] based on
(82, 82+18, large)-Net over F32 — Digital
Digital (82, 100, large)-net over F32, using
- t-expansion [i] based on digital (79, 100, large)-net over F32, using
(82, 82+18, large)-Net in Base 32 — Upper bound on s
There is no (82, 100, large)-net in base 32, because
- 16 times m-reduction [i] would yield (82, 84, large)-net in base 32, but