Best Known (59−50, 59, s)-Nets in Base 81
(59−50, 59, 172)-Net over F81 — Constructive and digital
Digital (9, 59, 172)-net over F81, using
- t-expansion [i] based on digital (7, 59, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
(59−50, 59, 244)-Net over F81 — Digital
Digital (9, 59, 244)-net over F81, using
- net from sequence [i] based on digital (9, 243)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 9 and N(F) ≥ 244, using
(59−50, 59, 4048)-Net in Base 81 — Upper bound on s
There is no (9, 59, 4049)-net in base 81, because
- the generalized Rao bound for nets shows that 81m ≥ 40109 253784 794061 132438 264972 495048 913008 210592 338340 822300 301211 497743 051691 942234 349606 124734 927284 052280 098001 > 8159 [i]