MinT - Best Known (141, 141+90, s)-Nets in Base 3

Best Known (141, 141+90, s)-Nets in Base 3

(141, 141+90, 156)-Net over F₃ — Constructive and digital

Digital (141, 231, 156)-net over F₃, using

7 times m-reduction [i] based on digital (141, 238, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 119, 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]

(141, 141+90, 228)-Net over F₃ — Digital

Digital (141, 231, 228)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(141, 141+90, 2435)-Net in Base 3 — Upper bound on s

There is no (141, 231, 2436)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 166 036423 270751 034490 020881 597442 531555 785473 278902 070677 360084 180474 335850 243619 655852 672565 752794 472131 122793 > 3²³¹ [i]