Best Known (45, 45+56, s)-Nets in Base 27
(45, 45+56, 176)-Net over F27 — Constructive and digital
Digital (45, 101, 176)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 35, 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 (10, 66, 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 (7, 35, 82)-net over F27, using
(45, 45+56, 340)-Net over F27 — Digital
Digital (45, 101, 340)-net over F27, using
(45, 45+56, 370)-Net in Base 27 — Constructive
(45, 101, 370)-net in base 27, using
- t-expansion [i] based on (43, 101, 370)-net in base 27, using
- 7 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
- 7 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(45, 45+56, 63250)-Net in Base 27 — Upper bound on s
There is no (45, 101, 63251)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3 696596 202457 321509 375621 755678 000884 708968 939539 680589 487270 374804 374851 986350 281511 663125 230605 624398 570075 481065 317964 042954 866370 603877 238921 > 27101 [i]