Best Known (75, 75+21, s)-Nets in Base 32
(75, 75+21, 104933)-Net over F32 — Constructive and digital
Digital (75, 96, 104933)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 15, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (60, 81, 104857)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 104857, F32, 21, 21) (dual of [(104857, 21), 2201916, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3281, 1048571, F32, 21) (dual of [1048571, 1048490, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
- an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 324−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- discarding factors / shortening the dual code based on linear OA(3281, 1048576, F32, 21) (dual of [1048576, 1048495, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3281, 1048571, F32, 21) (dual of [1048571, 1048490, 22]-code), using
- net defined by OOA [i] based on linear OOA(3281, 104857, F32, 21, 21) (dual of [(104857, 21), 2201916, 22]-NRT-code), using
- digital (5, 15, 76)-net over F32, using
(75, 75+21, 209748)-Net in Base 32 — Constructive
(75, 96, 209748)-net in base 32, using
- (u, u+v)-construction [i] based on
- digital (0, 10, 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
- (65, 86, 209715)-net in base 32, using
- net defined by OOA [i] based on OOA(3286, 209715, S32, 21, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3286, 2097151, S32, 21), using
- discarding factors based on OA(3286, 2097155, S32, 21), using
- discarding parts of the base [i] based on linear OA(12861, 2097155, F128, 21) (dual of [2097155, 2097094, 22]-code), using
- construction X applied to Ce(20) ⊂ Ce(19) [i] based on
- linear OA(12861, 2097152, F128, 21) (dual of [2097152, 2097091, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(12858, 2097152, F128, 20) (dual of [2097152, 2097094, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 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(20) ⊂ Ce(19) [i] based on
- discarding parts of the base [i] based on linear OA(12861, 2097155, F128, 21) (dual of [2097155, 2097094, 22]-code), using
- discarding factors based on OA(3286, 2097155, S32, 21), using
- OOA 10-folding and stacking with additional row [i] based on OA(3286, 2097151, S32, 21), using
- net defined by OOA [i] based on OOA(3286, 209715, S32, 21, 21), using
- digital (0, 10, 33)-net over F32, using
(75, 75+21, 4494335)-Net over F32 — Digital
Digital (75, 96, 4494335)-net over F32, using
(75, 75+21, large)-Net in Base 32 — Upper bound on s
There is no (75, 96, large)-net in base 32, because
- 19 times m-reduction [i] would yield (75, 77, large)-net in base 32, but