MinT - Best Known (69−30, 69, s)-Nets in Base 4

Best Known (69−30, 69, s)-Nets in Base 4

(69−30, 69, 90)-Net over F₄ — Constructive and digital

Digital (39, 69, 90)-net over F₄, using

1 times m-reduction [i] based on digital (39, 70, 90)-net over F₄, using
- trace code for nets [i] based on digital (4, 35, 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]

(69−30, 69, 95)-Net over F₄ — Digital

Digital (39, 69, 95)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(69−30, 69, 1247)-Net in Base 4 — Upper bound on s

There is no (39, 69, 1248)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 351276 160709 992252 063784 165852 872876 174981 > 4⁶⁹ [i]