Best Known (41, 41+62, s)-Nets in Base 27
(41, 41+62, 140)-Net over F27 — Constructive and digital
Digital (41, 103, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 35, 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 (6, 68, 76)-net over F27, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 6 and N(F) ≥ 76, using
- net from sequence [i] based on digital (6, 75)-sequence over F27, using
- digital (4, 35, 64)-net over F27, using
(41, 41+62, 224)-Net in Base 27 — Constructive
(41, 103, 224)-net in base 27, using
- t-expansion [i] based on (40, 103, 224)-net in base 27, using
- 5 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 81, 224)-net over F81, using
- 5 times m-reduction [i] based on (40, 108, 224)-net in base 27, using
(41, 41+62, 273)-Net over F27 — Digital
Digital (41, 103, 273)-net over F27, using
- t-expansion [i] based on digital (40, 103, 273)-net over F27, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 40 and N(F) ≥ 273, using
- net from sequence [i] based on digital (40, 272)-sequence over F27, using
(41, 41+62, 298)-Net in Base 27
(41, 103, 298)-net in base 27, using
- t-expansion [i] based on (39, 103, 298)-net in base 27, using
- 5 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 12 and N(F) ≥ 298, using
- net from sequence [i] based on digital (12, 297)-sequence over F81, using
- base change [i] based on digital (12, 81, 298)-net over F81, using
- 5 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
(41, 41+62, 27203)-Net in Base 27 — Upper bound on s
There is no (41, 103, 27204)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2696 359634 350244 811607 475706 219141 971507 401889 171506 219146 787240 970982 004947 630064 891089 516041 828047 385323 638907 120818 020435 593753 640858 707756 439825 > 27103 [i]