MinT - Best Known (70, 70+61, s)-Nets in Base 4

Best Known (70, 70+61, s)-Nets in Base 4

(70, 70+61, 90)-Net over F₄ — Constructive and digital

Digital (70, 131, 90)-net over F₄, using

1 times m-reduction [i] based on digital (70, 132, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 66, 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]

(70, 70+61, 125)-Net over F₄ — Digital

Digital (70, 131, 125)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+61, 1607)-Net in Base 4 — Upper bound on s

There is no (70, 131, 1608)-net in base 4, because

1 times m-reduction [i] would yield (70, 130, 1608)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 881281 204271 252434 636541 873984 290222 158462 258093 064301 619275 817642 438129 368712 > 4¹³⁰ [i]