Best Known (73−43, 73, s)-Nets in Base 81
(73−43, 73, 370)-Net over F81 — Constructive and digital
Digital (30, 73, 370)-net over F81, using
- t-expansion [i] based on digital (16, 73, 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
(73−43, 73, 551)-Net over F81 — Digital
Digital (30, 73, 551)-net over F81, using
- net from sequence [i] based on digital (30, 550)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 30 and N(F) ≥ 551, using
(73−43, 73, 379112)-Net in Base 81 — Upper bound on s
There is no (30, 73, 379113)-net in base 81, because
- 1 times m-reduction [i] would yield (30, 72, 379113)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 257593 503776 779889 099268 389913 673488 035780 232666 478163 348735 575317 634765 769824 085014 528240 610922 906669 781516 956496 225248 531063 600340 013841 > 8172 [i]