Best Known (20, 20+28, s)-Nets in Base 27
(20, 20+28, 112)-Net over F27 — Constructive and digital
Digital (20, 48, 112)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (2, 16, 48)-net over F27, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 2 and N(F) ≥ 48, using
- net from sequence [i] based on digital (2, 47)-sequence over F27, using
- digital (4, 32, 64)-net over F27, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 4 and N(F) ≥ 64, using
- net from sequence [i] based on digital (4, 63)-sequence over F27, using
- digital (2, 16, 48)-net over F27, using
(20, 20+28, 149)-Net over F27 — Digital
Digital (20, 48, 149)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2748, 149, F27, 2, 28) (dual of [(149, 2), 250, 29]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2746, 148, F27, 2, 28) (dual of [(148, 2), 250, 29]-NRT-code), using
- extended algebraic-geometric NRT-code AGe(2;F,267P) [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(2746, 148, F27, 2, 28) (dual of [(148, 2), 250, 29]-NRT-code), using
(20, 20+28, 172)-Net in Base 27 — Constructive
(20, 48, 172)-net in base 27, using
- 4 times m-reduction [i] based on (20, 52, 172)-net in base 27, using
- base change [i] based on digital (7, 39, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 39, 172)-net over F81, using
(20, 20+28, 226)-Net in Base 27
(20, 48, 226)-net in base 27, using
- base change [i] based on digital (8, 36, 226)-net over F81, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 8 and N(F) ≥ 226, using
- net from sequence [i] based on digital (8, 225)-sequence over F81, using
(20, 20+28, 18786)-Net in Base 27 — Upper bound on s
There is no (20, 48, 18787)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 507 574593 191813 667542 060155 688790 235737 239339 462930 668379 733891 097149 > 2748 [i]