Best Known (77−56, 77, s)-Nets in Base 27
(77−56, 77, 108)-Net over F27 — Constructive and digital
Digital (21, 77, 108)-net over F27, using
- t-expansion [i] based on digital (18, 77, 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
(77−56, 77, 163)-Net over F27 — Digital
Digital (21, 77, 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
(77−56, 77, 3737)-Net in Base 27 — Upper bound on s
There is no (21, 77, 3738)-net in base 27, because
- the generalized Rao bound for nets shows that 27m ≥ 164 551043 355264 521361 177329 058746 085620 588287 566205 219349 893090 925308 850503 277760 158649 321556 457592 043644 339993 > 2777 [i]