Best Known (29, 29+38, s)-Nets in Base 27
(29, 29+38, 140)-Net over F27 — Constructive and digital
Digital (29, 67, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 23, 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, 44, 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, 23, 64)-net over F27, using
(29, 29+38, 172)-Net in Base 27 — Constructive
(29, 67, 172)-net in base 27, using
- 21 times m-reduction [i] based on (29, 88, 172)-net in base 27, using
- base change [i] based on digital (7, 66, 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, 66, 172)-net over F81, using
(29, 29+38, 217)-Net over F27 — Digital
Digital (29, 67, 217)-net over F27, using
(29, 29+38, 298)-Net in Base 27
(29, 67, 298)-net in base 27, using
- 1 times m-reduction [i] based on (29, 68, 298)-net in base 27, using
- base change [i] based on digital (12, 51, 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, 51, 298)-net over F81, using
(29, 29+38, 34006)-Net in Base 27 — Upper bound on s
There is no (29, 67, 34007)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 797182 426928 156155 796551 486965 346394 768408 826161 366106 082347 581657 781678 311113 652954 507586 411315 > 2767 [i]