MinT - Best Known (43, 43+43, s)-Nets in Base 5

Best Known (43, 43+43, s)-Nets in Base 5

(43, 43+43, 78)-Net over F₅ — Constructive and digital

Digital (43, 86, 78)-net over F₅, using

t-expansion [i] based on digital (38, 86, 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]

(43, 43+43, 92)-Net over F₅ — Digital

Digital (43, 86, 92)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(43, 43+43, 1448)-Net in Base 5 — Upper bound on s

There is no (43, 86, 1449)-net in base 5, because

1 times m-reduction [i] would yield (43, 85, 1449)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 258511 833550 452679 349905 036397 089360 197424 980714 027778 445717 > 5⁸⁵ [i]