Best Known (42, 42+101, s)-Nets in Base 5
(42, 42+101, 78)-Net over F5 — Constructive and digital
Digital (42, 143, 78)-net over F5, using
- t-expansion [i] based on digital (38, 143, 78)-net over F5, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 38 and N(F) ≥ 78, using
- net from sequence [i] based on digital (38, 77)-sequence over F5, using
(42, 42+101, 80)-Net over F5 — Digital
Digital (42, 143, 80)-net over F5, using
- t-expansion [i] based on digital (41, 143, 80)-net over F5, using
- net from sequence [i] based on digital (41, 79)-sequence over F5, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F5 with g(F) = 41 and N(F) ≥ 80, using
- net from sequence [i] based on digital (41, 79)-sequence over F5, using
(42, 42+101, 434)-Net in Base 5 — Upper bound on s
There is no (42, 143, 435)-net in base 5, because
- 1 times m-reduction [i] would yield (42, 142, 435)-net in base 5, but
- the generalized Rao bound for nets shows that 5m ≥ 1867 198088 071203 212563 662923 540555 591148 061394 024805 449008 766109 717956 996280 611468 300616 904264 136121 > 5142 [i]