MinT - Best Known (73−35, 73, s)-Nets in Base 5

Best Known (73−35, 73, s)-Nets in Base 5

(73−35, 73, 78)-Net over F₅ — Constructive and digital

Digital (38, 73, 78)-net over F₅, using

net from sequence [i] based on digital (38, 77)-sequence over F₅, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 38 and N(F) ≥ 78, using
  - an explicitly constructive algebraic function field [i]

(73−35, 73, 94)-Net over F₅ — Digital

Digital (38, 73, 94)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(73−35, 73, 1625)-Net in Base 5 — Upper bound on s

There is no (38, 73, 1626)-net in base 5, because

1 times m-reduction [i] would yield (38, 72, 1626)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 212 943772 601919 781739 289847 601681 449149 361464 267625 > 5⁷² [i]