Best Known (70−50, 70, s)-Nets in Base 27
(70−50, 70, 108)-Net over F27 — Constructive and digital
Digital (20, 70, 108)-net over F27, using
- t-expansion [i] based on digital (18, 70, 108)-net over F27, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- F3 from the tower of function fields by Bezerra, GarcÃa, and Stichtenoth over F27 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 108, using
- net from sequence [i] based on digital (18, 107)-sequence over F27, using
(70−50, 70, 116)-Net in Base 27 — Constructive
(20, 70, 116)-net in base 27, using
- 2 times m-reduction [i] based on (20, 72, 116)-net in base 27, using
- base change [i] based on digital (2, 54, 116)-net over F81, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 2 and N(F) ≥ 116, using
- net from sequence [i] based on digital (2, 115)-sequence over F81, using
- base change [i] based on digital (2, 54, 116)-net over F81, using
(70−50, 70, 148)-Net over F27 — Digital
Digital (20, 70, 148)-net over F27, using
- t-expansion [i] based on digital (18, 70, 148)-net over F27, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 18 and N(F) ≥ 148, using
- net from sequence [i] based on digital (18, 147)-sequence over F27, using
(70−50, 70, 3972)-Net in Base 27 — Upper bound on s
There is no (20, 70, 3973)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 15739 454462 315313 707457 207537 451526 609990 800341 645093 596099 403262 796230 954189 496417 347719 656785 182435 > 2770 [i]