MinT - Best Known (71, 71+30, s)-Nets in Base 3

Best Known (71, 71+30, s)-Nets in Base 3

(71, 71+30, 156)-Net over F₃ — Constructive and digital

Digital (71, 101, 156)-net over F₃, using

1 times m-reduction [i] based on digital (71, 102, 156)-net over F₃, using
- trace code for nets [i] based on digital (3, 34, 52)-net over F₂₇, using
  - net from sequence [i] based on digital (3, 51)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 3 and N(F) ≥ 52, using
      - a function field by SÃ©mirat [i]

(71, 71+30, 264)-Net over F₃ — Digital

Digital (71, 101, 264)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 71+30, 5225)-Net in Base 3 — Upper bound on s

There is no (71, 101, 5226)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 547106 961216 984412 191312 282755 621331 356133 650297 > 3¹⁰¹ [i]