Best Known (45, 45+58, s)-Nets in Base 27
(45, 45+58, 170)-Net over F27 — Constructive and digital
Digital (45, 103, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 36, 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 (9, 67, 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 (7, 36, 82)-net over F27, using
(45, 45+58, 317)-Net over F27 — Digital
Digital (45, 103, 317)-net over F27, using
(45, 45+58, 370)-Net in Base 27 — Constructive
(45, 103, 370)-net in base 27, using
- t-expansion [i] based on (43, 103, 370)-net in base 27, using
- 5 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
- 5 times m-reduction [i] based on (43, 108, 370)-net in base 27, using
(45, 45+58, 54429)-Net in Base 27 — Upper bound on s
There is no (45, 103, 54430)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 2694 615520 575972 222600 559712 512712 943543 027591 012524 573805 985181 379884 052632 253433 156941 027493 335243 543896 822889 631099 599218 888342 850961 619502 127989 > 27103 [i]