MinT - Best Known (225−65, 225, s)-Nets in Base 3

Best Known (225−65, 225, s)-Nets in Base 3

(225−65, 225, 282)-Net over F₃ — Constructive and digital

Digital (160, 225, 282)-net over F₃, using

trace code for nets [i] based on digital (10, 75, 94)-net over F₂₇, using
- net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
    - a function field by SÃ©mirat [i]

(225−65, 225, 555)-Net over F₃ — Digital

Digital (160, 225, 555)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−65, 225, 13954)-Net in Base 3 — Upper bound on s

There is no (160, 225, 13955)-net in base 3, because

1 times m-reduction [i] would yield (160, 224, 13955)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75066 866116 005229 894872 311244 545682 206435 670261 731451 570971 060817 241513 386252 296066 817602 067527 980806 704577 > 3²²⁴ [i]