MinT - Best Known (92, 135, s)-Nets in Base 4

Best Known (92, 135, s)-Nets in Base 4

(92, 135, 240)-Net over F₄ — Constructive and digital

Digital (92, 135, 240)-net over F₄, using

t-expansion [i] based on digital (91, 135, 240)-net over F₄, using
- trace code for nets [i] based on digital (1, 45, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

(92, 135, 472)-Net over F₄ — Digital

Digital (92, 135, 472)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(92, 135, 20077)-Net in Base 4 — Upper bound on s

There is no (92, 135, 20078)-net in base 4, because

1 times m-reduction [i] would yield (92, 134, 20078)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 474 294553 657787 064216 318953 561720 628899 048189 286146 465910 155221 113086 749096 726990 > 4¹³⁴ [i]