Best Known (78−69, 78, s)-Nets in Base 81
(78−69, 78, 172)-Net over F81 — Constructive and digital
Digital (9, 78, 172)-net over F81, using
- t-expansion [i] based on digital (7, 78, 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
(78−69, 78, 244)-Net over F81 — Digital
Digital (9, 78, 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
(78−69, 78, 3535)-Net in Base 81 — Upper bound on s
There is no (9, 78, 3536)-net in base 81, because
- 1 times m-reduction [i] would yield (9, 77, 3536)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 901 064201 951060 191073 333390 448098 200568 152255 134531 510615 176702 519282 313978 745127 565269 766676 330012 991691 873447 382109 527228 423942 476431 645902 072321 > 8177 [i]