MinT - Best Known (222−51, 222, s)-Nets in Base 3

Best Known (222−51, 222, s)-Nets in Base 3

(222−51, 222, 600)-Net over F₃ — Constructive and digital

Digital (171, 222, 600)-net over F₃, using

3² times duplication [i] based on digital (169, 220, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 55, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(222−51, 222, 1304)-Net over F₃ — Digital

Digital (171, 222, 1304)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(222−51, 222, 83988)-Net in Base 3 — Upper bound on s

There is no (171, 222, 83989)-net in base 3, because

1 times m-reduction [i] would yield (171, 221, 83989)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2778 630325 744668 792574 322887 333765 747818 134886 409778 850312 937032 941152 038060 014281 954202 745451 271620 271691 > 3²²¹ [i]