Best Known (61−45, 61, s)-Nets in Base 8
(61−45, 61, 65)-Net over F8 — Constructive and digital
Digital (16, 61, 65)-net over F8, using
- t-expansion [i] based on digital (14, 61, 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
(61−45, 61, 362)-Net in Base 8 — Upper bound on s
There is no (16, 61, 363)-net in base 8, because
- 1 times m-reduction [i] would yield (16, 60, 363)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 1 614368 471772 093615 236412 489070 058048 173679 040398 079508 > 860 [i]