MinT - Best Known (60, 60+34, s)-Nets in Base 5

Best Known (60, 60+34, s)-Nets in Base 5

(60, 60+34, 252)-Net over F₅ — Constructive and digital

Digital (60, 94, 252)-net over F₅, using

6 times m-reduction [i] based on digital (60, 100, 252)-net over F₅, using
- trace code for nets [i] based on digital (10, 50, 126)-net over F₂₅, using
  - net from sequence [i] based on digital (10, 125)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 10 and N(F) ≥ 126, using
      - the Hermitian function field over F₂₅ [i]

(60, 60+34, 325)-Net over F₅ — Digital

Digital (60, 94, 325)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+34, 13133)-Net in Base 5 — Upper bound on s

There is no (60, 94, 13134)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 505336 988602 495930 463826 631906 764795 384007 919467 745116 383578 381625 > 5⁹⁴ [i]