Best Known (12, 12+61, s)-Nets in Base 81
(12, 12+61, 172)-Net over F81 — Constructive and digital
Digital (12, 73, 172)-net over F81, using
- t-expansion [i] based on digital (7, 73, 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+61, 298)-Net over F81 — Digital
Digital (12, 73, 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+61, 5713)-Net in Base 81 — Upper bound on s
There is no (12, 73, 5714)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 72, 5714)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 257693 149457 927435 128683 089465 584039 768430 862736 783413 799799 030366 994641 033070 610441 280161 957993 673227 107755 490858 284968 985859 155453 233601 > 8172 [i]