Best Known (12, 39, s)-Nets in Base 81
(12, 39, 172)-Net over F81 — Constructive and digital
Digital (12, 39, 172)-net over F81, using
- t-expansion [i] based on digital (7, 39, 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, 39, 298)-Net over F81 — Digital
Digital (12, 39, 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, 39, 26845)-Net in Base 81 — Upper bound on s
There is no (12, 39, 26846)-net in base 81, because
- 1 times m-reduction [i] would yield (12, 38, 26846)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3 331347 362650 248073 389633 867798 833935 737866 816639 936102 286069 488030 467041 > 8138 [i]