Best Known (32, 32+102, s)-Nets in Base 8
(32, 32+102, 65)-Net over F8 — Constructive and digital
Digital (32, 134, 65)-net over F8, using
- t-expansion [i] based on digital (14, 134, 65)-net over F8, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- the Suzuki function field over F8 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 14 and N(F) ≥ 65, using
- net from sequence [i] based on digital (14, 64)-sequence over F8, using
(32, 32+102, 97)-Net over F8 — Digital
Digital (32, 134, 97)-net over F8, using
- t-expansion [i] based on digital (28, 134, 97)-net over F8, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 28 and N(F) ≥ 97, using
- net from sequence [i] based on digital (28, 96)-sequence over F8, using
(32, 32+102, 637)-Net in Base 8 — Upper bound on s
There is no (32, 134, 638)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 10 796994 088391 170870 643254 341791 583513 108574 618467 483344 961485 578750 736671 964718 239636 411883 910456 375343 993641 038577 211258 > 8134 [i]