MinT - Best Known (74, 74+26, s)-Nets in Base 5

Best Known (74, 74+26, s)-Nets in Base 5

(74, 74+26, 306)-Net over F₅ — Constructive and digital

Digital (74, 100, 306)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (15, 28, 54)-net over F₅, using
  - trace code for nets [i] based on digital (1, 14, 27)-net over F₂₅, using
    - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
      - Niederreiter sequence [i]
2. digital (46, 72, 252)-net over F₅, using
  - trace code for nets [i] based on digital (10, 36, 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]

(74, 74+26, 1602)-Net over F₅ — Digital

Digital (74, 100, 1602)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 74+26, 337307)-Net in Base 5 — Upper bound on s

There is no (74, 100, 337308)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 7888 614491 487503 364867 986228 849397 334694 840643 466212 947451 707950 832625 > 5¹⁰⁰ [i]