MinT - Best Known (101−27, 101, s)-Nets in Base 5

Best Known (101−27, 101, s)-Nets in Base 5

(101−27, 101, 304)-Net over F₅ — Constructive and digital

Digital (74, 101, 304)-net over F₅, using

5¹ times duplication [i] based on digital (73, 100, 304)-net over F₅, using
- (u,Â u+v)-construction [i] based on
  1. digital (13, 26, 52)-net over F₅, using
    - trace code for nets [i] based on digital (0, 13, 26)-net over F₂₅, using
      - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
        Niederreiter sequence [i]
  2. digital (47, 74, 252)-net over F₅, using
    - trace code for nets [i] based on digital (10, 37, 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]

(101−27, 101, 1382)-Net over F₅ — Digital

Digital (74, 101, 1382)-net over F₅, using

Gilbertâ€“VarÅ¡amov bound [i]

(101−27, 101, 337307)-Net in Base 5 — Upper bound on s

There is no (74, 101, 337308)-net in base 5, because

1 times m-reduction [i] would yield (74, 100, 337308)-net in base 5, but
- 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]