Best Known (65, 101, s)-Nets in Base 32
(65, 101, 371)-Net over F32 — Constructive and digital
Digital (65, 101, 371)-net over F32, using
- 1 times m-reduction [i] based on digital (65, 102, 371)-net over F32, using
- generalized (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 (7, 19, 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, 25, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 44, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (5, 14, 77)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(65, 101, 910)-Net in Base 32 — Constructive
(65, 101, 910)-net in base 32, using
- 321 times duplication [i] based on (64, 100, 910)-net in base 32, using
- net defined by OOA [i] based on OOA(32100, 910, S32, 36, 36), using
- OA 18-folding and stacking [i] based on OA(32100, 16380, S32, 36), using
- discarding factors based on OA(32100, 16386, S32, 36), using
- discarding parts of the base [i] based on linear OA(12871, 16386, F128, 36) (dual of [16386, 16315, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(34) [i] based on
- linear OA(12871, 16384, F128, 36) (dual of [16384, 16313, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(12869, 16384, F128, 35) (dual of [16384, 16315, 36]-code), using an extension Ce(34) of the primitive narrow-sense BCH-code C(I) with length 16383 = 1282−1, defining interval I = [1,34], and designed minimum distance d ≥ |I|+1 = 35 [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(35) ⊂ Ce(34) [i] based on
- discarding parts of the base [i] based on linear OA(12871, 16386, F128, 36) (dual of [16386, 16315, 37]-code), using
- discarding factors based on OA(32100, 16386, S32, 36), using
- OA 18-folding and stacking [i] based on OA(32100, 16380, S32, 36), using
- net defined by OOA [i] based on OOA(32100, 910, S32, 36, 36), using
(65, 101, 9911)-Net over F32 — Digital
Digital (65, 101, 9911)-net over F32, using
(65, 101, large)-Net in Base 32 — Upper bound on s
There is no (65, 101, large)-net in base 32, because
- 34 times m-reduction [i] would yield (65, 67, large)-net in base 32, but