MinT - Best Known (39, 39+81, s)-Nets in Base 5

Best Known (39, 39+81, s)-Nets in Base 5

(39, 39+81, 78)-Net over F₅ — Constructive and digital

Digital (39, 120, 78)-net over F₅, using

t-expansion [i] based on digital (38, 120, 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]

(39, 39+81, 444)-Net in Base 5 — Upper bound on s

There is no (39, 120, 445)-net in base 5, because

1 times m-reduction [i] would yield (39, 119, 445)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 157370 125482 244843 557231 809801 319840 289818 648525 643289 674489 653985 226485 930570 734177 > 5¹¹⁹ [i]