MinT - Best Known (159, 159+67, s)-Nets in Base 3

Best Known (159, 159+67, s)-Nets in Base 3

(159, 159+67, 252)-Net over F₃ — Constructive and digital

Digital (159, 226, 252)-net over F₃, using

3¹ times duplication [i] based on digital (158, 225, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 75, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(159, 159+67, 512)-Net over F₃ — Digital

Digital (159, 226, 512)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(159, 159+67, 11755)-Net in Base 3 — Upper bound on s

There is no (159, 226, 11756)-net in base 3, because

1 times m-reduction [i] would yield (159, 225, 11756)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 225626 862982 261806 523441 255863 153414 969824 307243 238917 608406 294333 617217 405867 224258 984467 839456 555554 048985 > 3²²⁵ [i]