Best Known (57−36, 57, s)-Nets in Base 27
(57−36, 57, 108)-Net over F27 — Constructive and digital
Digital (21, 57, 108)-net over F27, using
- t-expansion [i] based on digital (18, 57, 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
(57−36, 57, 160)-Net in Base 27 — Constructive
(21, 57, 160)-net in base 27, using
- 7 times m-reduction [i] based on (21, 64, 160)-net in base 27, using
- base change [i] based on digital (5, 48, 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, 48, 160)-net over F81, using
(57−36, 57, 163)-Net over F27 — Digital
Digital (21, 57, 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
(57−36, 57, 190)-Net in Base 27
(21, 57, 190)-net in base 27, using
- 3 times m-reduction [i] based on (21, 60, 190)-net in base 27, using
- base change [i] based on digital (6, 45, 190)-net over F81, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F81 with g(F) = 6 and N(F) ≥ 190, using
- net from sequence [i] based on digital (6, 189)-sequence over F81, using
- base change [i] based on digital (6, 45, 190)-net over F81, using
(57−36, 57, 9894)-Net in Base 27 — Upper bound on s
There is no (21, 57, 9895)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 3871 870671 554960 940121 472025 385195 581275 132509 620997 156999 642581 578974 472525 120253 > 2757 [i]