Best Known (145−62, 145, s)-Nets in Base 5
(145−62, 145, 252)-Net over F5 — Constructive and digital
Digital (83, 145, 252)-net over F5, using
- 1 times m-reduction [i] based on digital (83, 146, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 73, 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, 73, 126)-net over F25, using
(145−62, 145, 5749)-Net in Base 5 — Upper bound on s
There is no (83, 145, 5750)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 224713 151776 794995 325226 930568 850995 195697 619242 739046 637027 629499 217116 132276 705141 482901 535289 168121 > 5145 [i]