Best Known (15, 15+77, s)-Nets in Base 8
(15, 15+77, 65)-Net over F8 — Constructive and digital
Digital (15, 92, 65)-net over F8, using
- t-expansion [i] based on digital (14, 92, 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
(15, 15+77, 288)-Net in Base 8 — Upper bound on s
There is no (15, 92, 289)-net in base 8, because
- 1 times m-reduction [i] would yield (15, 91, 289)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 15612 322234 848331 880601 230359 684924 233263 993047 381795 871050 142694 117687 977369 078400 > 891 [i]