Best Known (51−33, 51, s)-Nets in Base 27
(51−33, 51, 108)-Net over F27 — Constructive and digital
Digital (18, 51, 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
(51−33, 51, 148)-Net over F27 — Digital
Digital (18, 51, 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
(51−33, 51, 160)-Net in Base 27 — Constructive
(18, 51, 160)-net in base 27, using
- 1 times m-reduction [i] based on (18, 52, 160)-net in base 27, using
- base change [i] based on digital (5, 39, 160)-net over F81, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 160, using
- net from sequence [i] based on digital (5, 159)-sequence over F81, using
- base change [i] based on digital (5, 39, 160)-net over F81, using
(51−33, 51, 167)-Net in Base 27
(18, 51, 167)-net in base 27, using
- 1 times m-reduction [i] based on (18, 52, 167)-net in base 27, using
- base change [i] based on digital (5, 39, 167)-net over F81, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 5 and N(F) ≥ 167, using
- net from sequence [i] based on digital (5, 166)-sequence over F81, using
- base change [i] based on digital (5, 39, 167)-net over F81, using
(51−33, 51, 7764)-Net in Base 27 — Upper bound on s
There is no (18, 51, 7765)-net in base 27, because
- 1 times m-reduction [i] would yield (18, 50, 7765)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 370232 067386 630173 530452 941852 616292 608098 745821 886908 453499 450269 293633 > 2750 [i]