MinT - Best Known (63−34, 63, s)-Nets in Base 5

Best Known (63−34, 63, s)-Nets in Base 5

(63−34, 63, 51)-Net over F₅ — Constructive and digital

Digital (29, 63, 51)-net over F₅, using

t-expansion [i] based on digital (22, 63, 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]

(63−34, 63, 57)-Net over F₅ — Digital

Digital (29, 63, 57)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(63−34, 63, 686)-Net in Base 5 — Upper bound on s

There is no (29, 63, 687)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 110 125305 038387 740525 584472 901435 468960 320125 > 5⁶³ [i]