Best Known (11, 68, s)-Nets in Base 81
(11, 68, 172)-Net over F81 — Constructive and digital
Digital (11, 68, 172)-net over F81, using
- t-expansion [i] based on digital (7, 68, 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
(11, 68, 244)-Net over F81 — Digital
Digital (11, 68, 244)-net over F81, using
- t-expansion [i] based on digital (9, 68, 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
(11, 68, 5193)-Net in Base 81 — Upper bound on s
There is no (11, 68, 5194)-net in base 81, because
- 1 times m-reduction [i] would yield (11, 67, 5194)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 73 926325 055484 300203 015069 594527 011266 720848 834067 938916 205621 195167 568896 076689 023823 922911 126735 110217 066716 293435 781242 162561 > 8167 [i]