Best Known (45, 45+48, s)-Nets in Base 27
(45, 45+48, 190)-Net over F27 — Constructive and digital
Digital (45, 93, 190)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (10, 34, 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 (11, 59, 96)-net over F27, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 11 and N(F) ≥ 96, using
- net from sequence [i] based on digital (11, 95)-sequence over F27, using
- digital (10, 34, 94)-net over F27, using
(45, 45+48, 370)-Net in Base 27 — Constructive
(45, 93, 370)-net in base 27, using
- t-expansion [i] based on (43, 93, 370)-net in base 27, using
- 15 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
- 15 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(45, 45+48, 485)-Net over F27 — Digital
Digital (45, 93, 485)-net over F27, using
(45, 45+48, 132703)-Net in Base 27 — Upper bound on s
There is no (45, 93, 132704)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 13 087198 753065 857044 962675 257987 716097 789573 597584 935841 119545 082467 905739 167015 927358 645174 433350 905324 725027 468486 864129 694327 259137 > 2793 [i]