Best Known (50−26, 50, s)-Nets in Base 27
(50−26, 50, 146)-Net over F27 — Constructive and digital
Digital (24, 50, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 17, 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 (7, 33, 82)-net over F27, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 7 and N(F) ≥ 82, using
- net from sequence [i] based on digital (7, 81)-sequence over F27, using
- digital (4, 17, 64)-net over F27, using
(50−26, 50, 172)-Net in Base 27 — Constructive
(24, 50, 172)-net in base 27, using
- 18 times m-reduction [i] based on (24, 68, 172)-net in base 27, using
- base change [i] based on digital (7, 51, 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, 51, 172)-net over F81, using
(50−26, 50, 305)-Net over F27 — Digital
Digital (24, 50, 305)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2750, 305, F27, 26) (dual of [305, 255, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2750, 364, F27, 26) (dual of [364, 314, 27]-code), using
(50−26, 50, 69765)-Net in Base 27 — Upper bound on s
There is no (24, 50, 69766)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 370057 228609 673482 145242 703543 643052 769583 272665 901842 949474 340338 559717 > 2750 [i]