Best Known (78−45, 78, s)-Nets in Base 81
(78−45, 78, 370)-Net over F81 — Constructive and digital
Digital (33, 78, 370)-net over F81, using
- t-expansion [i] based on digital (16, 78, 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
(78−45, 78, 576)-Net over F81 — Digital
Digital (33, 78, 576)-net over F81, using
- net from sequence [i] based on digital (33, 575)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 33 and N(F) ≥ 576, using
(78−45, 78, 541317)-Net in Base 81 — Upper bound on s
There is no (33, 78, 541318)-net in base 81, because
- 1 times m-reduction [i] would yield (33, 77, 541318)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 898 168066 867422 836436 558783 911612 210320 435046 965899 922819 390244 932918 530652 162768 486111 421789 870021 895895 965272 793123 911347 021040 583606 687161 046081 > 8177 [i]