Best Known (63−55, 63, s)-Nets in Base 81
(63−55, 63, 172)-Net over F81 — Constructive and digital
Digital (8, 63, 172)-net over F81, using
- t-expansion [i] based on digital (7, 63, 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
(63−55, 63, 226)-Net over F81 — Digital
Digital (8, 63, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
(63−55, 63, 3280)-Net in Base 81 — Upper bound on s
There is no (8, 63, 3281)-net in base 81, because
- 1 times m-reduction [i] would yield (8, 62, 3281)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 21190 818140 497820 045704 455249 697453 024263 248885 843395 882313 346101 757050 970981 863487 787358 705369 689232 383545 693578 101361 > 8162 [i]