MinT - Best Known (112−33, 112, s)-Nets in Base 3

Best Known (112−33, 112, s)-Nets in Base 3

(112−33, 112, 192)-Net over F₃ — Constructive and digital

Digital (79, 112, 192)-net over F₃, using

3¹ times duplication [i] based on digital (78, 111, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 37, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(112−33, 112, 293)-Net over F₃ — Digital

Digital (79, 112, 293)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112−33, 112, 6927)-Net in Base 3 — Upper bound on s

There is no (79, 112, 6928)-net in base 3, because

1 times m-reduction [i] would yield (79, 111, 6928)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 91432 561918 792497 271428 992788 654953 687910 343332 041729 > 3¹¹¹ [i]