Best Known (81, 81+19, s)-Nets in Base 32
(81, 81+19, 932099)-Net over F32 — Constructive and digital
Digital (81, 100, 932099)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 9, 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 (72, 91, 932066)-net over F32, using
- net defined by OOA [i] based on linear OOA(3291, 932066, F32, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3291, 8388595, F32, 19) (dual of [8388595, 8388504, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(3291, large, F32, 19) (dual of [large, large−91, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3291, large, F32, 19) (dual of [large, large−91, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(3291, 8388595, F32, 19) (dual of [8388595, 8388504, 20]-code), using
- net defined by OOA [i] based on linear OOA(3291, 932066, F32, 19, 19) (dual of [(932066, 19), 17709163, 20]-NRT-code), using
- digital (0, 9, 33)-net over F32, using
(81, 81+19, 932146)-Net in Base 32 — Constructive
(81, 100, 932146)-net in base 32, using
- (u, u+v)-construction [i] based on
- (3, 12, 80)-net in base 32, using
- base change [i] based on digital (1, 10, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- base change [i] based on digital (1, 10, 80)-net over F64, using
- (69, 88, 932066)-net in base 32, using
- base change [i] based on digital (36, 55, 932066)-net over F256, using
- net defined by OOA [i] based on linear OOA(25655, 932066, F256, 19, 19) (dual of [(932066, 19), 17709199, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25655, 8388595, F256, 19) (dual of [8388595, 8388540, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(25655, large, F256, 19) (dual of [large, large−55, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(25655, 8388595, F256, 19) (dual of [8388595, 8388540, 20]-code), using
- net defined by OOA [i] based on linear OOA(25655, 932066, F256, 19, 19) (dual of [(932066, 19), 17709199, 20]-NRT-code), using
- base change [i] based on digital (36, 55, 932066)-net over F256, using
- (3, 12, 80)-net in base 32, using
(81, 81+19, large)-Net over F32 — Digital
Digital (81, 100, large)-net over F32, using
- t-expansion [i] based on digital (79, 100, large)-net over F32, using
(81, 81+19, large)-Net in Base 32 — Upper bound on s
There is no (81, 100, large)-net in base 32, because
- 17 times m-reduction [i] would yield (81, 83, large)-net in base 32, but