Best Known (31, 96, s)-Nets in Base 8
(31, 96, 65)-Net over F8 — Constructive and digital
Digital (31, 96, 65)-net over F8, using
- t-expansion [i] based on digital (14, 96, 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
(31, 96, 97)-Net over F8 — Digital
Digital (31, 96, 97)-net over F8, using
- t-expansion [i] based on digital (28, 96, 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
(31, 96, 856)-Net in Base 8 — Upper bound on s
There is no (31, 96, 857)-net in base 8, because
- 1 times m-reduction [i] would yield (31, 95, 857)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 62 787301 131109 820322 799468 642626 072357 160851 091924 197071 586972 558661 244385 477449 741490 > 895 [i]