Best Known (69, 108, s)-Nets in Base 3
(69, 108, 128)-Net over F3 — Constructive and digital
Digital (69, 108, 128)-net over F3, using
- 4 times m-reduction [i] based on digital (69, 112, 128)-net over F3, using
- trace code for nets [i] based on digital (13, 56, 64)-net over F9, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 13 and N(F) ≥ 64, using
- net from sequence [i] based on digital (13, 63)-sequence over F9, using
- trace code for nets [i] based on digital (13, 56, 64)-net over F9, using
(69, 108, 151)-Net over F3 — Digital
Digital (69, 108, 151)-net over F3, using
(69, 108, 1909)-Net in Base 3 — Upper bound on s
There is no (69, 108, 1910)-net in base 3, because
- 1 times m-reduction [i] would yield (69, 107, 1910)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1130 660779 961560 831815 221217 777678 530634 477732 254081 > 3107 [i]