MinT - Best Known (80, 135, s)-Nets in Base 4

Best Known (80, 135, s)-Nets in Base 4

(80, 135, 130)-Net over F₄ — Constructive and digital

Digital (80, 135, 130)-net over F₄, using

13 times m-reduction [i] based on digital (80, 148, 130)-net over F₄, using
- trace code for nets [i] based on digital (6, 74, 65)-net over F₁₆, using
  - net from sequence [i] based on digital (6, 64)-sequence over F₁₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 6 and N(F) ≥ 65, using
      - the Hermitian function field over F₁₆ [i]

(80, 135, 197)-Net over F₄ — Digital

Digital (80, 135, 197)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(80, 135, 3520)-Net in Base 4 — Upper bound on s

There is no (80, 135, 3521)-net in base 4, because

1 times m-reduction [i] would yield (80, 134, 3521)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 476 583173 280084 392409 434531 673178 760813 001217 371526 027436 633907 392046 003795 563584 > 4¹³⁴ [i]