MinT - Best Known (112, 112+49, s)-Nets in Base 3

Best Known (112, 112+49, s)-Nets in Base 3

(112, 112+49, 192)-Net over F₃ — Constructive and digital

Digital (112, 161, 192)-net over F₃, using

1 times m-reduction [i] based on digital (112, 162, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 54, 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, 112+49, 352)-Net over F₃ — Digital

Digital (112, 161, 352)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+49, 7409)-Net in Base 3 — Upper bound on s

There is no (112, 161, 7410)-net in base 3, because

1 times m-reduction [i] would yield (112, 160, 7410)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21908 418844 255931 477225 615514 744198 637302 376373 059019 340903 444990 287516 355057 > 3¹⁶⁰ [i]