Best Known (28, 70, s)-Nets in Base 32
(28, 70, 131)-Net over F32 — Constructive and digital
Digital (28, 70, 131)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (0, 21, 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 (7, 49, 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 (0, 21, 33)-net over F32, using
(28, 70, 257)-Net over F32 — Digital
Digital (28, 70, 257)-net over F32, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
(28, 70, 258)-Net in Base 32 — Constructive
(28, 70, 258)-net in base 32, using
- 2 times m-reduction [i] based on (28, 72, 258)-net in base 32, using
- base change [i] based on digital (1, 45, 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, 45, 258)-net over F256, using
(28, 70, 289)-Net in Base 32
(28, 70, 289)-net in base 32, using
- 2 times m-reduction [i] based on (28, 72, 289)-net in base 32, using
- base change [i] based on digital (1, 45, 289)-net over F256, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 1 and N(F) ≥ 289, using
- net from sequence [i] based on digital (1, 288)-sequence over F256, using
- base change [i] based on digital (1, 45, 289)-net over F256, using
(28, 70, 29116)-Net in Base 32 — Upper bound on s
There is no (28, 70, 29117)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2294 427653 143959 166957 978314 678376 115814 392644 728470 309294 936772 319688 609229 476839 348778 599096 916790 140776 > 3270 [i]