Best Known (97−58, 97, s)-Nets in Base 27
(97−58, 97, 140)-Net over F27 — Constructive and digital
Digital (39, 97, 140)-net over F27, using
- (u, u+v)-construction [i] based on
- digital (4, 33, 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, 64, 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, 33, 64)-net over F27, using
(97−58, 97, 224)-Net in Base 27 — Constructive
(39, 97, 224)-net in base 27, using
- 7 times m-reduction [i] based on (39, 104, 224)-net in base 27, using
- base change [i] based on digital (13, 78, 224)-net over F81, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 13 and N(F) ≥ 224, using
- net from sequence [i] based on digital (13, 223)-sequence over F81, using
- base change [i] based on digital (13, 78, 224)-net over F81, using
(97−58, 97, 271)-Net over F27 — Digital
Digital (39, 97, 271)-net over F27, using
- net from sequence [i] based on digital (39, 270)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 39 and N(F) ≥ 271, using
(97−58, 97, 298)-Net in Base 27
(39, 97, 298)-net in base 27, using
- 11 times m-reduction [i] based on (39, 108, 298)-net in base 27, using
- base change [i] based on digital (12, 81, 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, 81, 298)-net over F81, using
(97−58, 97, 27515)-Net in Base 27 — Upper bound on s
There is no (39, 97, 27516)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 6 959496 342401 612776 998682 208918 327732 661313 628403 063655 732957 499033 057430 846651 686552 399293 446685 669002 834114 485475 599214 006306 684428 157817 > 2797 [i]