Best Known (72−49, 72, s)-Nets in Base 81
(72−49, 72, 370)-Net over F81 — Constructive and digital
Digital (23, 72, 370)-net over F81, using
- t-expansion [i] based on digital (16, 72, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
(72−49, 72, 54214)-Net in Base 81 — Upper bound on s
There is no (23, 72, 54215)-net in base 81, because
- 1 times m-reduction [i] would yield (23, 71, 54215)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3181 188215 816598 236548 392469 892110 272441 596777 787823 831113 469792 724729 444411 053798 758704 045894 631696 171830 976582 056832 705857 699574 940801 > 8171 [i]