Best Known (49−37, 49, s)-Nets in Base 8
(49−37, 49, 48)-Net over F8 — Constructive and digital
Digital (12, 49, 48)-net over F8, using
- t-expansion [i] based on digital (11, 49, 48)-net over F8, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 11 and N(F) ≥ 48, using
- net from sequence [i] based on digital (11, 47)-sequence over F8, using
(49−37, 49, 49)-Net over F8 — Digital
Digital (12, 49, 49)-net over F8, using
- net from sequence [i] based on digital (12, 48)-sequence over F8, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F8 with g(F) = 12 and N(F) ≥ 49, using
(49−37, 49, 265)-Net in Base 8 — Upper bound on s
There is no (12, 49, 266)-net in base 8, because
- 1 times m-reduction [i] would yield (12, 48, 266)-net in base 8, but
- the generalized Rao bound for nets shows that 8m ≥ 23 346352 636179 116468 297793 298676 056034 353600 > 848 [i]