MinT - Best Known (81−40, 81, s)-Nets in Base 5

Best Known (81−40, 81, s)-Nets in Base 5

(81−40, 81, 78)-Net over F₅ — Constructive and digital

Digital (41, 81, 78)-net over F₅, using

t-expansion [i] based on digital (38, 81, 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]

(81−40, 81, 92)-Net over F₅ — Digital

Digital (41, 81, 92)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(81−40, 81, 1391)-Net in Base 5 — Upper bound on s

There is no (41, 81, 1392)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 414 512736 808412 417354 019194 764604 460513 801962 764359 092225 > 5⁸¹ [i]