Best Known (62, 62+14, s)-Nets in Base 32
(62, 62+14, 1198437)-Net over F32 — Constructive and digital
Digital (62, 76, 1198437)-net over F32, using
- (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 (52, 66, 1198371)-net over F32, using
- net defined by OOA [i] based on linear OOA(3266, 1198371, F32, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3266, 8388597, F32, 14) (dual of [8388597, 8388531, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3266, large, F32, 14) (dual of [large, large−66, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 33554431 = 325−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(3266, large, F32, 14) (dual of [large, large−66, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3266, 8388597, F32, 14) (dual of [8388597, 8388531, 15]-code), using
- net defined by OOA [i] based on linear OOA(3266, 1198371, F32, 14, 14) (dual of [(1198371, 14), 16777128, 15]-NRT-code), using
- digital (3, 10, 66)-net over F32, using
(62, 62+14, 1198628)-Net in Base 32 — Constructive
(62, 76, 1198628)-net in base 32, using
- (u, u+v)-construction [i] based on
- (5, 12, 257)-net in base 32, using
- base change [i] based on (3, 10, 257)-net in base 64, using
- 2 times m-reduction [i] based on (3, 12, 257)-net in base 64, using
- base change [i] based on digital (0, 9, 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, 9, 257)-net over F256, using
- 2 times m-reduction [i] based on (3, 12, 257)-net in base 64, using
- base change [i] based on (3, 10, 257)-net in base 64, using
- (50, 64, 1198371)-net in base 32, using
- base change [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- base change [i] based on digital (26, 40, 1198371)-net over F256, using
- (5, 12, 257)-net in base 32, using
(62, 62+14, large)-Net over F32 — Digital
Digital (62, 76, large)-net over F32, using
- t-expansion [i] based on digital (60, 76, large)-net over F32, using
(62, 62+14, large)-Net in Base 32 — Upper bound on s
There is no (62, 76, large)-net in base 32, because
- 12 times m-reduction [i] would yield (62, 64, large)-net in base 32, but