MinT - Best Known (40, 40+36, s)-Nets in Base 5

Best Known (40, 40+36, s)-Nets in Base 5

(40, 40+36, 78)-Net over F₅ — Constructive and digital

Digital (40, 76, 78)-net over F₅, using

t-expansion [i] based on digital (38, 76, 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]

(40, 40+36, 101)-Net over F₅ — Digital

Digital (40, 76, 101)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(40, 40+36, 1674)-Net in Base 5 — Upper bound on s

There is no (40, 76, 1675)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 132823 615520 393689 607716 239741 687298 536162 646445 930041 > 5⁷⁶ [i]