MinT - Best Known (54, 101, s)-Nets in Base 4

Best Known (54, 101, s)-Nets in Base 4

(54, 101, 76)-Net over F₄ — Constructive and digital

Digital (54, 101, 76)-net over F₄, using

1 times m-reduction [i] based on digital (54, 102, 76)-net over F₄, using
- trace code for nets [i] based on digital (3, 51, 38)-net over F₁₆, using
  - net from sequence [i] based on digital (3, 37)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 3 and N(F) ≥ 38, using
      - a function field by SÃ©mirat [i]

(54, 101, 102)-Net over F₄ — Digital

Digital (54, 101, 102)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(54, 101, 1284)-Net in Base 4 — Upper bound on s

There is no (54, 101, 1285)-net in base 4, because

1 times m-reduction [i] would yield (54, 100, 1285)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 619350 692815 688511 732721 780916 424344 770759 814261 814623 587584 > 4¹⁰⁰ [i]