MinT - Best Known (60−31, 60, s)-Nets in Base 5

Best Known (60−31, 60, s)-Nets in Base 5

(60−31, 60, 51)-Net over F₅ — Constructive and digital

Digital (29, 60, 51)-net over F₅, using

t-expansion [i] based on digital (22, 60, 51)-net over F₅, using
- net from sequence [i] based on digital (22, 50)-sequence over F₅, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 22 and N(F) ≥ 51, using
    - an explicitly constructive algebraic function field [i]

(60−31, 60, 63)-Net over F₅ — Digital

Digital (29, 60, 63)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60−31, 60, 890)-Net in Base 5 — Upper bound on s

There is no (29, 60, 891)-net in base 5, because

1 times m-reduction [i] would yield (29, 59, 891)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 173922 884780 195581 323435 495024 173875 868149 > 5⁵⁹ [i]