Best Known (25, 25+50, s)-Nets in Base 81
(25, 25+50, 370)-Net over F81 — Constructive and digital
Digital (25, 75, 370)-net over F81, using
- t-expansion [i] based on digital (16, 75, 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
(25, 25+50, 392)-Net over F81 — Digital
Digital (25, 75, 392)-net over F81, using
- net from sequence [i] based on digital (25, 391)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 25 and N(F) ≥ 392, using
(25, 25+50, 67594)-Net in Base 81 — Upper bound on s
There is no (25, 75, 67595)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 136913 330311 804470 044599 006329 286904 306822 726411 991546 389926 510892 538929 905907 344133 732437 167052 452757 120258 879327 537559 575914 389102 010650 390001 > 8175 [i]