Best Known (54, 54+30, s)-Nets in Base 32
(54, 54+30, 338)-Net over F32 — Constructive and digital
Digital (54, 84, 338)-net over F32, using
- 1 times m-reduction [i] based on digital (54, 85, 338)-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 (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 (7, 22, 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, 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
- generalized (u, u+v)-construction [i] based on
(54, 54+30, 1092)-Net in Base 32 — Constructive
(54, 84, 1092)-net in base 32, using
- base change [i] based on digital (30, 60, 1092)-net over F128, using
- 1 times m-reduction [i] based on digital (30, 61, 1092)-net over F128, using
- net defined by OOA [i] based on linear OOA(12861, 1092, F128, 31, 31) (dual of [(1092, 31), 33791, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12861, 16381, F128, 31) (dual of [16381, 16320, 32]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(12861, 16384, F128, 31) (dual of [16384, 16323, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(12861, 16381, F128, 31) (dual of [16381, 16320, 32]-code), using
- net defined by OOA [i] based on linear OOA(12861, 1092, F128, 31, 31) (dual of [(1092, 31), 33791, 32]-NRT-code), using
- 1 times m-reduction [i] based on digital (30, 61, 1092)-net over F128, using
(54, 54+30, 8634)-Net over F32 — Digital
Digital (54, 84, 8634)-net over F32, using
(54, 54+30, large)-Net in Base 32 — Upper bound on s
There is no (54, 84, large)-net in base 32, because
- 28 times m-reduction [i] would yield (54, 56, large)-net in base 32, but