Best Known (58, 58+40, s)-Nets in Base 32
(58, 58+40, 316)-Net over F32 — Constructive and digital
Digital (58, 98, 316)-net over F32, using
- 1 times m-reduction [i] based on digital (58, 99, 316)-net over F32, using
- generalized (u, u+v)-construction [i] based on
- digital (7, 20, 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, 27, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (11, 52, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (7, 20, 98)-net over F32, using
- generalized (u, u+v)-construction [i] based on
(58, 58+40, 515)-Net in Base 32 — Constructive
(58, 98, 515)-net in base 32, using
- (u, u+v)-construction [i] based on
- (12, 32, 257)-net in base 32, using
- base change [i] based on digital (0, 20, 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, 20, 257)-net over F256, using
- (26, 66, 258)-net in base 32, using
- base change [i] based on (15, 55, 258)-net in base 64, using
- 1 times m-reduction [i] based on (15, 56, 258)-net in base 64, using
- base change [i] based on digital (1, 42, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- base change [i] based on digital (1, 42, 258)-net over F256, using
- 1 times m-reduction [i] based on (15, 56, 258)-net in base 64, using
- base change [i] based on (15, 55, 258)-net in base 64, using
- (12, 32, 257)-net in base 32, using
(58, 58+40, 3027)-Net over F32 — Digital
Digital (58, 98, 3027)-net over F32, using
(58, 58+40, 6355924)-Net in Base 32 — Upper bound on s
There is no (58, 98, 6355925)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3196 674389 622823 026873 665573 894576 725021 826679 267672 684734 918306 246071 562545 881057 763900 133616 764846 155289 467244 478320 858451 897641 957342 952205 149541 > 3298 [i]