MinT - Best Known (115−53, 115, s)-Nets in Base 4

Best Known (115−53, 115, s)-Nets in Base 4

(115−53, 115, 90)-Net over F₄ — Constructive and digital

Digital (62, 115, 90)-net over F₄, using

1 times m-reduction [i] based on digital (62, 116, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 58, 45)-net over F₁₆, using
  - net from sequence [i] based on digital (4, 44)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 4 and N(F) ≥ 45, using
      - a function field by GarcÃa and Quoos [i]

(115−53, 115, 117)-Net over F₄ — Digital

Digital (62, 115, 117)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(115−53, 115, 1513)-Net in Base 4 — Upper bound on s

There is no (62, 115, 1514)-net in base 4, because

1 times m-reduction [i] would yield (62, 114, 1514)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 435 267711 914861 698527 835877 264821 764543 777187 448853 969018 532808 010592 > 4¹¹⁴ [i]