MinT - Best Known (40, 40+82, s)-Nets in Base 5

Best Known (40, 40+82, s)-Nets in Base 5

(40, 40+82, 78)-Net over F₅ — Constructive and digital

Digital (40, 122, 78)-net over F₅, using

t-expansion [i] based on digital (38, 122, 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+82, 455)-Net in Base 5 — Upper bound on s

There is no (40, 122, 456)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 19 833076 773038 783897 773798 245605 121102 963287 240099 821282 350260 755852 982483 112099 931425 > 5¹²² [i]