MinT - Best Known (225−96, 225, s)-Nets in Base 3

Best Known (225−96, 225, s)-Nets in Base 3

(225−96, 225, 128)-Net over F₃ — Constructive and digital

Digital (129, 225, 128)-net over F₃, using

7 times m-reduction [i] based on digital (129, 232, 128)-net over F₃, using
- trace code for nets [i] based on digital (13, 116, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(225−96, 225, 173)-Net over F₃ — Digital

Digital (129, 225, 173)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−96, 225, 1568)-Net in Base 3 — Upper bound on s

There is no (129, 225, 1569)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 228965 984854 027665 081226 555816 879980 839166 258310 216542 442525 559487 783201 168018 878933 037166 914838 062161 776065 > 3²²⁵ [i]