Best Known (12, 12+53, s)-Nets in Base 81
(12, 12+53, 172)-Net over F81 — Constructive and digital
Digital (12, 65, 172)-net over F81, using
- t-expansion [i] based on digital (7, 65, 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
(12, 12+53, 298)-Net over F81 — Digital
Digital (12, 65, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
(12, 12+53, 6563)-Net in Base 81 — Upper bound on s
There is no (12, 65, 6564)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 64, 6564)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 139 038686 976599 354629 912623 133193 625089 319383 594276 454068 742411 102733 387820 362163 952386 490159 065536 495448 645132 535804 053121 > 8164 [i]