Best Known (49−39, 49, s)-Nets in Base 81
(49−39, 49, 172)-Net over F81 — Constructive and digital
Digital (10, 49, 172)-net over F81, using
- t-expansion [i] based on digital (7, 49, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(49−39, 49, 244)-Net over F81 — Digital
Digital (10, 49, 244)-net over F81, using
- t-expansion [i] based on digital (9, 49, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
(49−39, 49, 6560)-Net in Base 81 — Upper bound on s
There is no (10, 49, 6561)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 48, 6561)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 40 518387 688623 397135 769186 139057 116504 423993 899652 026022 750135 745820 236850 648964 690997 051121 > 8148 [i]