MinT - Best Known (60, 60+24, s)-Nets in Base 5

Best Known (60, 60+24, s)-Nets in Base 5

(60, 60+24, 270)-Net over F₅ — Constructive and digital

Digital (60, 84, 270)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (4, 16, 18)-net over F₅, using
  - net from sequence [i] based on digital (4, 17)-sequence over F₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₅ with g(F) = 4 and N(F) ≥ 18, using
      - an explicitly constructive algebraic function field [i]
2. digital (44, 68, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 34, 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+24, 853)-Net over F₅ — Digital

Digital (60, 84, 853)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(60, 60+24, 103289)-Net in Base 5 — Upper bound on s

There is no (60, 84, 103290)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 51702 447327 948800 250832 976046 633397 222220 565919 423527 719361 > 5⁸⁴ [i]