MinT - Best Known (112−31, 112, s)-Nets in Base 3

Best Known (112−31, 112, s)-Nets in Base 3

(112−31, 112, 228)-Net over F₃ — Constructive and digital

Digital (81, 112, 228)-net over F₃, using

3¹ times duplication [i] based on digital (80, 111, 228)-net over F₃, using
- trace code for nets [i] based on digital (6, 37, 76)-net over F₂₇, using
  - net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
      - a function field by SÃ©mirat [i]

(112−31, 112, 367)-Net over F₃ — Digital

Digital (81, 112, 367)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−31, 112, 10885)-Net in Base 3 — Upper bound on s

There is no (81, 112, 10886)-net in base 3, because

1 times m-reduction [i] would yield (81, 111, 10886)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91335 957671 757523 584273 107673 578118 741717 047629 474761 > 3¹¹¹ [i]