Best Known (80, 138, s)-Nets in Base 5
(80, 138, 252)-Net over F5 — Constructive and digital
Digital (80, 138, 252)-net over F5, using
- 2 times m-reduction [i] based on digital (80, 140, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 70, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- trace code for nets [i] based on digital (10, 70, 126)-net over F25, using
(80, 138, 6161)-Net in Base 5 — Upper bound on s
There is no (80, 138, 6162)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 2 873657 950186 069125 690746 137429 996427 204207 139120 821612 234390 623335 004862 155681 849323 571355 932745 > 5138 [i]