Best Known (72−51, 72, s)-Nets in Base 81
(72−51, 72, 370)-Net over F81 — Constructive and digital
Digital (21, 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
(72−51, 72, 33455)-Net in Base 81 — Upper bound on s
There is no (21, 72, 33456)-net in base 81, because
- 1 times m-reduction [i] would yield (21, 71, 33456)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 3180 160893 300754 497239 339727 805855 618839 323381 243488 716047 827307 896887 131613 896846 942200 796232 241805 648590 654925 833800 581888 718100 832001 > 8171 [i]