MinT - Best Known (49−25, 49, s)-Nets in Base 5

Best Known (49−25, 49, s)-Nets in Base 5

(49−25, 49, 51)-Net over F₅ — Constructive and digital

Digital (24, 49, 51)-net over F₅, using

t-expansion [i] based on digital (22, 49, 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]

(49−25, 49, 58)-Net over F₅ — Digital

Digital (24, 49, 58)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(49−25, 49, 817)-Net in Base 5 — Upper bound on s

There is no (24, 49, 818)-net in base 5, because

1 times m-reduction [i] would yield (24, 48, 818)-net in base 5, but
- the generalized Rao bound for nets shows that 5^mÂ â‰¥ 3557 094056 593442 699857 491135 297473 > 5⁴⁸ [i]