Best Known (75, 75+17, s)-Nets in Base 32
(75, 75+17, 1048639)-Net over F32 — Constructive and digital
Digital (75, 92, 1048639)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (3, 11, 64)-net over F32, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 3 and N(F) ≥ 64, using
- net from sequence [i] based on digital (3, 63)-sequence over F32, using
- digital (64, 81, 1048575)-net over F32, using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 33554433 | 3210−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(3281, large, F32, 17) (dual of [large, large−81, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(3281, 8388601, F32, 17) (dual of [8388601, 8388520, 18]-code), using
- net defined by OOA [i] based on linear OOA(3281, 1048575, F32, 17, 17) (dual of [(1048575, 17), 17825694, 18]-NRT-code), using
- digital (3, 11, 64)-net over F32, using
(75, 75+17, 1048832)-Net in Base 32 — Constructive
(75, 92, 1048832)-net in base 32, using
- (u, u+v)-construction [i] based on
- (6, 14, 257)-net in base 32, using
- 2 times m-reduction [i] based on (6, 16, 257)-net in base 32, using
- base change [i] based on digital (0, 10, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 10, 257)-net over F256, using
- 2 times m-reduction [i] based on (6, 16, 257)-net in base 32, using
- (61, 78, 1048575)-net in base 32, using
- base change [i] based on digital (48, 65, 1048575)-net over F64, using
- net defined by OOA [i] based on linear OOA(6465, 1048575, F64, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(6465, 8388601, F64, 17) (dual of [8388601, 8388536, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 648−1, defining interval I = [0,8], and minimum distance d ≥ |{−8,−7,…,8}|+1 = 18 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(6465, large, F64, 17) (dual of [large, large−65, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(6465, 8388601, F64, 17) (dual of [8388601, 8388536, 18]-code), using
- net defined by OOA [i] based on linear OOA(6465, 1048575, F64, 17, 17) (dual of [(1048575, 17), 17825710, 18]-NRT-code), using
- base change [i] based on digital (48, 65, 1048575)-net over F64, using
- (6, 14, 257)-net in base 32, using
(75, 75+17, large)-Net over F32 — Digital
Digital (75, 92, large)-net over F32, using
- 3 times m-reduction [i] based on digital (75, 95, large)-net over F32, using
(75, 75+17, large)-Net in Base 32 — Upper bound on s
There is no (75, 92, large)-net in base 32, because
- 15 times m-reduction [i] would yield (75, 77, large)-net in base 32, but