MinT - Best Known (180, 180+50, s)-Nets in Base 3

Best Known (180, 180+50, s)-Nets in Base 3

(180, 180+50, 688)-Net over F₃ — Constructive and digital

Digital (180, 230, 688)-net over F₃, using

3² times duplication [i] based on digital (178, 228, 688)-net over F₃, using
- trace code for nets [i] based on digital (7, 57, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

(180, 180+50, 1683)-Net over F₃ — Digital

Digital (180, 230, 1683)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(180, 180+50, 124745)-Net in Base 3 — Upper bound on s

There is no (180, 230, 124746)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 54 689244 546721 711781 286203 137070 515899 227637 251806 379202 861927 079814 486960 045151 525727 149157 472120 584119 090981 > 3²³⁰ [i]