Best Known (22, 44, s)-Nets in Base 27
(22, 44, 146)-Net over F27 — Constructive and digital
Digital (22, 44, 146)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 15, 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, 29, 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, 15, 64)-net over F27, using
(22, 44, 172)-Net in Base 27 — Constructive
(22, 44, 172)-net in base 27, using
- 16 times m-reduction [i] based on (22, 60, 172)-net in base 27, using
- base change [i] based on digital (7, 45, 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, 45, 172)-net over F81, using
(22, 44, 373)-Net over F27 — Digital
Digital (22, 44, 373)-net over F27, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2744, 373, F27, 22) (dual of [373, 329, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(2744, 728, F27, 22) (dual of [728, 684, 23]-code), using
(22, 44, 100339)-Net in Base 27 — Upper bound on s
There is no (22, 44, 100340)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 955 046150 378189 494042 749058 167827 780578 868800 863569 828660 953233 > 2744 [i]