MinT - Best Known (70, 70+24, s)-Nets in Base 5

Best Known (70, 70+24, s)-Nets in Base 5

(70, 70+24, 306)-Net over F₅ — Constructive and digital

Digital (70, 94, 306)-net over F₅, using

(u,Â u+v)-construction [i] based on
1. digital (14, 26, 54)-net over F₅, using
  - trace code for nets [i] based on digital (1, 13, 27)-net over F₂₅, using
    - net from sequence [i] based on digital (1, 26)-sequence over F₂₅, using
      - Niederreiter sequence [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]

(70, 70+24, 1706)-Net over F₅ — Digital

Digital (70, 94, 1706)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+24, 394963)-Net in Base 5 — Upper bound on s

There is no (70, 94, 394964)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 504876 594247 032642 425201 867198 164569 166821 507131 119958 711065 484033 > 5⁹⁴ [i]