MinT - Best Known (92−45, 92, s)-Nets in Base 5

Best Known (92−45, 92, s)-Nets in Base 5

(92−45, 92, 78)-Net over F₅ — Constructive and digital

Digital (47, 92, 78)-net over F₅, using

t-expansion [i] based on digital (38, 92, 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]

(92−45, 92, 105)-Net over F₅ — Digital

Digital (47, 92, 105)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(92−45, 92, 1745)-Net in Base 5 — Upper bound on s

There is no (47, 92, 1746)-net in base 5, because

1 times m-reduction [i] would yield (47, 91, 1746)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 4040 175723 467653 440679 397188 468987 398703 768089 232148 979586 676225 > 5⁹¹ [i]