MinT - Best Known (225−66, 225, s)-Nets in Base 3

Best Known (225−66, 225, s)-Nets in Base 3

(225−66, 225, 264)-Net over F₃ — Constructive and digital

Digital (159, 225, 264)-net over F₃, using

trace code for nets [i] based on digital (9, 75, 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]

(225−66, 225, 528)-Net over F₃ — Digital

Digital (159, 225, 528)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−66, 225, 11755)-Net in Base 3 — Upper bound on s

There is no (159, 225, 11756)-net in base 3, because

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]