Best Known (68, 68+49, s)-Nets in Base 3
(68, 68+49, 80)-Net over F3 — Constructive and digital
Digital (68, 117, 80)-net over F3, using
- 3 times m-reduction [i] based on digital (68, 120, 80)-net over F3, using
- trace code for nets [i] based on digital (8, 60, 40)-net over F9, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F9 with g(F) = 8 and N(F) ≥ 40, using
- net from sequence [i] based on digital (8, 39)-sequence over F9, using
- trace code for nets [i] based on digital (8, 60, 40)-net over F9, using
(68, 68+49, 105)-Net over F3 — Digital
Digital (68, 117, 105)-net over F3, using
(68, 68+49, 968)-Net in Base 3 — Upper bound on s
There is no (68, 117, 969)-net in base 3, because
- 1 times m-reduction [i] would yield (68, 116, 969)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 22 445723 404786 541243 217238 204001 032745 441226 665766 346209 > 3116 [i]