Best Known (35−29, 35, s)-Nets in Base 81
(35−29, 35, 160)-Net over F81 — Constructive and digital
Digital (6, 35, 160)-net over F81, using
- t-expansion [i] based on digital (5, 35, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
(35−29, 35, 190)-Net over F81 — Digital
Digital (6, 35, 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
(35−29, 35, 3253)-Net in Base 81 — Upper bound on s
There is no (6, 35, 3254)-net in base 81, because
- 1 times m-reduction [i] would yield (6, 34, 3254)-net in base 81, but
- the generalized Rao bound for nets shows that 81m ≥ 77473 174779 157887 454450 522595 775170 022540 387529 392019 736041 628481 > 8134 [i]