Best Known (40, 40+42, s)-Nets in Base 27
(40, 40+42, 182)-Net over F27 — Constructive and digital
Digital (40, 82, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 30, 88)-net over F27, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 9 and N(F) ≥ 88, using
- net from sequence [i] based on digital (9, 87)-sequence over F27, using
- digital (10, 52, 94)-net over F27, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 10 and N(F) ≥ 94, using
- net from sequence [i] based on digital (10, 93)-sequence over F27, using
- digital (9, 30, 88)-net over F27, using
(40, 40+42, 370)-Net in Base 27 — Constructive
(40, 82, 370)-net in base 27, using
- 14 times m-reduction [i] based on (40, 96, 370)-net in base 27, using
- base change [i] based on digital (16, 72, 370)-net over F81, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 16 and N(F) ≥ 370, using
- net from sequence [i] based on digital (16, 369)-sequence over F81, using
- base change [i] based on digital (16, 72, 370)-net over F81, using
(40, 40+42, 463)-Net over F27 — Digital
Digital (40, 82, 463)-net over F27, using
(40, 40+42, 129603)-Net in Base 27 — Upper bound on s
There is no (40, 82, 129604)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2354 200230 015329 941743 408002 262273 586067 419307 316942 821211 538349 706563 096876 280667 783497 249387 927586 154721 184555 905225 > 2782 [i]