Best Known (72−51, 72, s)-Nets in Base 27
(72−51, 72, 108)-Net over F27 — Constructive and digital
Digital (21, 72, 108)-net over F27, using
- t-expansion [i] based on digital (18, 72, 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
(72−51, 72, 116)-Net in Base 27 — Constructive
(21, 72, 116)-net in base 27, using
- 4 times m-reduction [i] based on (21, 76, 116)-net in base 27, using
- base change [i] based on digital (2, 57, 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, 57, 116)-net over F81, using
(72−51, 72, 163)-Net over F27 — Digital
Digital (21, 72, 163)-net over F27, using
- net from sequence [i] based on digital (21, 162)-sequence over F27, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F27 with g(F) = 21 and N(F) ≥ 163, using
(72−51, 72, 4534)-Net in Base 27 — Upper bound on s
There is no (21, 72, 4535)-net in base 27, because
- 1 times m-reduction [i] would yield (21, 71, 4535)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 425684 341910 561106 617650 114181 761965 574921 828024 236849 842519 576927 774439 285374 611628 407314 834703 107623 > 2771 [i]