Best Known (48, 48+58, s)-Nets in Base 27
(48, 48+58, 182)-Net over F27 — Constructive and digital
Digital (48, 106, 182)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (9, 38, 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, 68, 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, 38, 88)-net over F27, using
(48, 48+58, 370)-Net in Base 27 — Constructive
(48, 106, 370)-net in base 27, using
- t-expansion [i] based on (43, 106, 370)-net in base 27, using
- 2 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
- base change [i] based on digital (16, 81, 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, 81, 370)-net over F81, using
- 2 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(48, 48+58, 381)-Net over F27 — Digital
Digital (48, 106, 381)-net over F27, using
(48, 48+58, 76549)-Net in Base 27 — Upper bound on s
There is no (48, 106, 76550)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 53 037794 947888 584576 791340 586355 292799 984246 154309 506941 240703 787856 830913 220038 832468 843834 894293 057244 339913 777676 672845 598394 907327 361732 266289 596613 > 27106 [i]