Best Known (45, 45+42, s)-Nets in Base 3
(45, 45+42, 48)-Net over F3 — Constructive and digital
Digital (45, 87, 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
(45, 45+42, 57)-Net over F3 — Digital
Digital (45, 87, 57)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(387, 57, F3, 5, 42) (dual of [(57, 5), 198, 43]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(382, 56, F3, 5, 42) (dual of [(56, 5), 198, 43]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(5;F,237P) [i] based on function field F/F3 with g(F) = 40 and N(F) ≥ 56, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(382, 56, F3, 5, 42) (dual of [(56, 5), 198, 43]-NRT-code), using
(45, 45+42, 391)-Net in Base 3 — Upper bound on s
There is no (45, 87, 392)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 337286 240605 917635 005694 659315 253984 787345 > 387 [i]