Best Known (62−43, 62, s)-Nets in Base 8
(62−43, 62, 65)-Net over F8 — Constructive and digital
Digital (19, 62, 65)-net over F8, using
- t-expansion [i] based on digital (14, 62, 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
(62−43, 62, 507)-Net in Base 8 — Upper bound on s
There is no (19, 62, 508)-net in base 8, because
- 1 times m-reduction [i] would yield (19, 61, 508)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 12 318456 335848 597883 461792 138738 171460 085557 935348 387434 > 861 [i]