MinT - Best Known (232−68, 232, s)-Nets in Base 3

Best Known (232−68, 232, s)-Nets in Base 3

(232−68, 232, 264)-Net over F₃ — Constructive and digital

Digital (164, 232, 264)-net over F₃, using

3¹ times duplication [i] based on digital (163, 231, 264)-net over F₃, using
- trace code for nets [i] based on digital (9, 77, 88)-net over F₂₇, using
  - net from sequence [i] based on digital (9, 87)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 88, using
      - a function field by SÃ©mirat [i]

(232−68, 232, 544)-Net over F₃ — Digital

Digital (164, 232, 544)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−68, 232, 12159)-Net in Base 3 — Upper bound on s

There is no (164, 232, 12160)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 493 371166 044908 352165 331864 164459 025946 165162 581349 251508 861770 191786 854336 805055 303222 432485 136206 451276 070145 > 3²³² [i]