MinT - Best Known (39, 39+51, s)-Nets in Base 5

Best Known (39, 39+51, s)-Nets in Base 5

(39, 39+51, 78)-Net over F₅ — Constructive and digital

Digital (39, 90, 78)-net over F₅, using

t-expansion [i] based on digital (38, 90, 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+51, 765)-Net in Base 5 — Upper bound on s

There is no (39, 90, 766)-net in base 5, because

1 times m-reduction [i] would yield (39, 89, 766)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 166 007047 939255 355998 852165 121152 523802 171161 825252 619901 885945 > 5⁸⁹ [i]