Best Known (70−63, 70, s)-Nets in Base 81
(70−63, 70, 172)-Net over F81 — Constructive and digital
Digital (7, 70, 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
(70−63, 70, 190)-Net over F81 — Digital
Digital (7, 70, 190)-net over F81, using
- t-expansion [i] based on digital (6, 70, 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
(70−63, 70, 2731)-Net in Base 81 — Upper bound on s
There is no (7, 70, 2732)-net in base 81, because
- 1 times m-reduction [i] would yield (7, 69, 2732)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 486635 154999 827987 130758 727829 232861 218319 622405 936845 240754 394985 101422 569382 617070 063846 151739 323897 515853 477438 474380 194340 663361 > 8169 [i]