MinT - Best Known (26, 53, s)-Nets in Base 5

Best Known (26, 53, s)-Nets in Base 5

(26, 53, 51)-Net over F₅ — Constructive and digital

Digital (26, 53, 51)-net over F₅, using

t-expansion [i] based on digital (22, 53, 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]

(26, 53, 61)-Net over F₅ — Digital

Digital (26, 53, 61)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(26, 53, 876)-Net in Base 5 — Upper bound on s

There is no (26, 53, 877)-net in base 5, because

1 times m-reduction [i] would yield (26, 52, 877)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 2 241332 737993 982833 483668 285937 837125 > 5⁵² [i]