Best Known (58−39, 58, s)-Nets in Base 81
(58−39, 58, 370)-Net over F81 — Constructive and digital
Digital (19, 58, 370)-net over F81, using
- t-expansion [i] based on digital (16, 58, 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
(58−39, 58, 52662)-Net in Base 81 — Upper bound on s
There is no (19, 58, 52663)-net in base 81, because
- 1 times m-reduction [i] would yield (19, 57, 52663)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 6 076712 113545 276126 364894 029864 165024 296260 638931 240897 161741 672013 954204 550943 628446 189636 652911 781938 838161 > 8157 [i]