Best Known (79, 79+54, s)-Nets in Base 5
(79, 79+54, 252)-Net over F5 — Constructive and digital
Digital (79, 133, 252)-net over F5, using
- 5 times m-reduction [i] based on digital (79, 138, 252)-net over F5, using
- trace code for nets [i] based on digital (10, 69, 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, 69, 126)-net over F25, using
(79, 79+54, 274)-Net over F5 — Digital
Digital (79, 133, 274)-net over F5, using
(79, 79+54, 7555)-Net in Base 5 — Upper bound on s
There is no (79, 133, 7556)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 918 545206 330552 909969 429725 983010 350587 474237 967634 686589 439388 911023 613362 268596 625577 061905 > 5133 [i]