Best Known (109−62, 109, s)-Nets in Base 27
(109−62, 109, 170)-Net over F27 — Constructive and digital
Digital (47, 109, 170)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (7, 38, 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, 71, 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, 38, 82)-net over F27, using
(109−62, 109, 314)-Net over F27 — Digital
Digital (47, 109, 314)-net over F27, using
(109−62, 109, 370)-Net in Base 27 — Constructive
(47, 109, 370)-net in base 27, using
- 271 times duplication [i] based on (46, 108, 370)-net in base 27, using
- t-expansion [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
- t-expansion [i] based on (43, 108, 370)-net in base 27, using
(109−62, 109, 51497)-Net in Base 27 — Upper bound on s
There is no (47, 109, 51498)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 1 044444 730564 652198 185867 320743 732455 713375 452931 566433 248729 111285 000698 208703 894458 708736 518764 447651 599158 554416 819979 164537 464934 485635 293480 773415 098569 > 27109 [i]