Best Known (53, 53+87, s)-Nets in Base 3
(53, 53+87, 48)-Net over F3 — Constructive and digital
Digital (53, 140, 48)-net over F3, using
- t-expansion [i] based on digital (45, 140, 48)-net over F3, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 45 and N(F) ≥ 48, using
- net from sequence [i] based on digital (45, 47)-sequence over F3, using
(53, 53+87, 64)-Net over F3 — Digital
Digital (53, 140, 64)-net over F3, using
- t-expansion [i] based on digital (49, 140, 64)-net over F3, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 49 and N(F) ≥ 64, using
- net from sequence [i] based on digital (49, 63)-sequence over F3, using
(53, 53+87, 254)-Net in Base 3 — Upper bound on s
There is no (53, 140, 255)-net in base 3, because
- 1 times m-reduction [i] would yield (53, 139, 255)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 2 364734 599210 192552 334661 578247 365513 696400 675493 678530 871864 247211 > 3139 [i]