MinT - Best Known (44, 44+39, s)-Nets in Base 5

Best Known (44, 44+39, s)-Nets in Base 5

(44, 44+39, 78)-Net over F₅ — Constructive and digital

Digital (44, 83, 78)-net over F₅, using

t-expansion [i] based on digital (38, 83, 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]

(44, 44+39, 111)-Net over F₅ — Digital

Digital (44, 83, 111)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+39, 2045)-Net in Base 5 — Upper bound on s

There is no (44, 83, 2046)-net in base 5, because

1 times m-reduction [i] would yield (44, 82, 2046)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2071 992831 880266 709622 864869 014493 628885 061403 999394 081305 > 5⁸² [i]