Best Known (31, 73, s)-Nets in Base 27
(31, 73, 140)-Net over F27 — Constructive and digital
Digital (31, 73, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 25, 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, 48, 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, 25, 64)-net over F27, using
(31, 73, 172)-Net in Base 27 — Constructive
(31, 73, 172)-net in base 27, using
- 23 times m-reduction [i] based on (31, 96, 172)-net in base 27, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 7 and N(F) ≥ 172, using
- net from sequence [i] based on digital (7, 171)-sequence over F81, using
- base change [i] based on digital (7, 72, 172)-net over F81, using
(31, 73, 214)-Net over F27 — Digital
Digital (31, 73, 214)-net over F27, using
(31, 73, 298)-Net in Base 27
(31, 73, 298)-net in base 27, using
- 3 times m-reduction [i] based on (31, 76, 298)-net in base 27, using
- base change [i] based on digital (12, 57, 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, 57, 298)-net over F81, using
(31, 73, 31554)-Net in Base 27 — Upper bound on s
There is no (31, 73, 31555)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 308 781437 348436 245977 015267 623302 800827 871064 707320 724417 865005 684871 893393 639467 646373 763552 867146 477511 > 2773 [i]