MinT - Best Known (83−42, 83, s)-Nets in Base 5

Best Known (83−42, 83, s)-Nets in Base 5

(83−42, 83, 78)-Net over F₅ — Constructive and digital

Digital (41, 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]

(83−42, 83, 86)-Net over F₅ — Digital

Digital (41, 83, 86)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(83−42, 83, 1240)-Net in Base 5 — Upper bound on s

There is no (41, 83, 1241)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 10352 162523 742714 351085 399445 190062 436712 283323 740599 651925 > 5⁸³ [i]