MinT - Best Known (121−56, 121, s)-Nets in Base 4

Best Known (121−56, 121, s)-Nets in Base 4

(121−56, 121, 90)-Net over F₄ — Constructive and digital

Digital (65, 121, 90)-net over F₄, using

1 times m-reduction [i] based on digital (65, 122, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 61, 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]

(121−56, 121, 120)-Net over F₄ — Digital

Digital (65, 121, 120)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(121−56, 121, 1482)-Net in Base 4 — Upper bound on s

There is no (65, 121, 1483)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7 111155 408171 268336 993143 911712 563175 609359 812277 961809 691407 842997 106160 > 4¹²¹ [i]