MinT - Best Known (136−58, 136, s)-Nets in Base 3

Best Known (136−58, 136, s)-Nets in Base 3

(136−58, 136, 80)-Net over F₃ — Constructive and digital

Digital (78, 136, 80)-net over F₃, using

4 times m-reduction [i] based on digital (78, 140, 80)-net over F₃, using
- trace code for nets [i] based on digital (8, 70, 40)-net over F₉, using
  - net from sequence [i] based on digital (8, 39)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
      - a function field by SÃ©mirat [i]

(136−58, 136, 113)-Net over F₃ — Digital

Digital (78, 136, 113)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(136−58, 136, 980)-Net in Base 3 — Upper bound on s

There is no (78, 136, 981)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 79119 219221 455769 210859 810675 313628 029784 277158 043577 976370 095451 > 3¹³⁶ [i]