Best Known (87−31, 87, s)-Nets in Base 32
(87−31, 87, 360)-Net over F32 — Constructive and digital
Digital (56, 87, 360)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (3, 10, 66)-net over F32, using
- (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, 7, 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
- (u, u+v)-construction [i] based on
- digital (7, 17, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (7, 22, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 38, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (3, 10, 66)-net over F32, using
(87−31, 87, 1092)-Net in Base 32 — Constructive
(56, 87, 1092)-net in base 32, using
- 321 times duplication [i] based on (55, 86, 1092)-net in base 32, using
- net defined by OOA [i] based on OOA(3286, 1092, S32, 31, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(3286, 16381, S32, 31), using
- discarding factors based on OA(3286, 16386, S32, 31), using
- discarding parts of the base [i] based on linear OA(12861, 16386, F128, 31) (dual of [16386, 16325, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(29) [i] based on
- linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(12859, 16384, F128, 30) (dual of [16384, 16325, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [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(30) ⊂ Ce(29) [i] based on
- discarding parts of the base [i] based on linear OA(12861, 16386, F128, 31) (dual of [16386, 16325, 32]-code), using
- discarding factors based on OA(3286, 16386, S32, 31), using
- OOA 15-folding and stacking with additional row [i] based on OA(3286, 16381, S32, 31), using
- net defined by OOA [i] based on OOA(3286, 1092, S32, 31, 31), using
(87−31, 87, 9017)-Net over F32 — Digital
Digital (56, 87, 9017)-net over F32, using
(87−31, 87, large)-Net in Base 32 — Upper bound on s
There is no (56, 87, large)-net in base 32, because
- 29 times m-reduction [i] would yield (56, 58, large)-net in base 32, but