Best Known (61−51, 61, s)-Nets in Base 81
(61−51, 61, 172)-Net over F81 — Constructive and digital
Digital (10, 61, 172)-net over F81, using
- t-expansion [i] based on digital (7, 61, 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
(61−51, 61, 244)-Net over F81 — Digital
Digital (10, 61, 244)-net over F81, using
- t-expansion [i] based on digital (9, 61, 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
(61−51, 61, 4828)-Net in Base 81 — Upper bound on s
There is no (10, 61, 4829)-net in base 81, because
- 1 times m-reduction [i] would yield (10, 60, 4829)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3 240918 517433 775535 493244 060091 753872 894243 583799 784235 241414 013633 678686 465015 984475 552177 909421 714070 949452 858001 > 8160 [i]