MinT - Best Known (112, 112+48, s)-Nets in Base 3

Best Known (112, 112+48, s)-Nets in Base 3

(112, 112+48, 204)-Net over F₃ — Constructive and digital

Digital (112, 160, 204)-net over F₃, using

3¹ times duplication [i] based on digital (111, 159, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 53, 68)-net over F₂₇, using
  - net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
      - a function field by SÃ©mirat [i]

(112, 112+48, 366)-Net over F₃ — Digital

Digital (112, 160, 366)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(112, 112+48, 7409)-Net in Base 3 — Upper bound on s

There is no (112, 160, 7410)-net in base 3, because

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]