MinT - Best Known (131−36, 131, s)-Nets in Base 4

Best Known (131−36, 131, s)-Nets in Base 4

(131−36, 131, 531)-Net over F₄ — Constructive and digital

Digital (95, 131, 531)-net over F₄, using

1 times m-reduction [i] based on digital (95, 132, 531)-net over F₄, using
- trace code for nets [i] based on digital (7, 44, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

(131−36, 131, 848)-Net over F₄ — Digital

Digital (95, 131, 848)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(131−36, 131, 60612)-Net in Base 4 — Upper bound on s

There is no (95, 131, 60613)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 411315 075623 867218 576809 036666 972772 264653 635991 071451 939405 165026 787152 357880 > 4¹³¹ [i]