Best Known (34, 34+46, s)-Nets in Base 81
(34, 34+46, 370)-Net over F81 — Constructive and digital
Digital (34, 80, 370)-net over F81, using
- t-expansion [i] based on digital (16, 80, 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
(34, 34+46, 594)-Net over F81 — Digital
Digital (34, 80, 594)-net over F81, using
- net from sequence [i] based on digital (34, 593)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 34 and N(F) ≥ 594, using
(34, 34+46, 512348)-Net in Base 81 — Upper bound on s
There is no (34, 80, 512349)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 477 321357 316781 894214 949435 974187 740847 185096 114654 667629 349896 361673 782486 455293 318399 361105 595819 669120 712324 535181 351819 774840 360695 592682 820052 962161 > 8180 [i]