Best Known (60−53, 60, s)-Nets in Base 81
(60−53, 60, 172)-Net over F81 — Constructive and digital
Digital (7, 60, 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
(60−53, 60, 190)-Net over F81 — Digital
Digital (7, 60, 190)-net over F81, using
- t-expansion [i] based on digital (6, 60, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
(60−53, 60, 2812)-Net in Base 81 — Upper bound on s
There is no (7, 60, 2813)-net in base 81, because
- 1 times m-reduction [i] would yield (7, 59, 2813)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 40220 910966 717922 670521 688034 327523 759094 004632 349961 307404 740258 983738 289916 020714 591476 184855 395883 928547 131041 > 8159 [i]