Best Known (56−37, 56, s)-Nets in Base 27
(56−37, 56, 108)-Net over F27 — Constructive and digital
Digital (19, 56, 108)-net over F27, using
- t-expansion [i] based on digital (18, 56, 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
(56−37, 56, 148)-Net over F27 — Digital
Digital (19, 56, 148)-net over F27, using
- t-expansion [i] based on digital (18, 56, 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
(56−37, 56, 160)-Net in Base 27 — Constructive
(19, 56, 160)-net in base 27, using
- base change [i] based on digital (5, 42, 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
(56−37, 56, 167)-Net in Base 27
(19, 56, 167)-net in base 27, using
- base change [i] based on digital (5, 42, 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
(56−37, 56, 6857)-Net in Base 27 — Upper bound on s
There is no (19, 56, 6858)-net in base 27, because
- 1 times m-reduction [i] would yield (19, 55, 6858)-net in base 27, but
- the generalized Rao bound for nets shows that 27m ≥ 5 311311 473010 464313 115059 638955 336775 599208 106125 598238 581697 339470 872683 774565 > 2755 [i]