MinT - Best Known (136, 221, s)-Nets in Base 3

Best Known (136, 221, s)-Nets in Base 3

(136, 221, 156)-Net over F₃ — Constructive and digital

Digital (136, 221, 156)-net over F₃, using

7 times m-reduction [i] based on digital (136, 228, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 114, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(136, 221, 228)-Net over F₃ — Digital

Digital (136, 221, 228)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136, 221, 2564)-Net in Base 3 — Upper bound on s

There is no (136, 221, 2565)-net in base 3, because

1 times m-reduction [i] would yield (136, 220, 2565)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 929 164134 332374 676124 322416 008902 903854 544730 755912 591979 837331 325461 528329 083388 300013 455188 250127 389297 > 3²²⁰ [i]