MinT - Best Known (117, 117+52, s)-Nets in Base 3

Best Known (117, 117+52, s)-Nets in Base 3

(117, 117+52, 192)-Net over F₃ — Constructive and digital

Digital (117, 169, 192)-net over F₃, using

3¹ times duplication [i] based on digital (116, 168, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 56, 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]

(117, 117+52, 354)-Net over F₃ — Digital

Digital (117, 169, 354)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(117, 117+52, 6635)-Net in Base 3 — Upper bound on s

There is no (117, 169, 6636)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 430 491584 317884 375903 668617 955872 775770 854754 654492 818899 134581 705015 566298 229929 > 3¹⁶⁹ [i]