MinT - Best Known (243−86, 243, s)-Nets in Base 3

Best Known (243−86, 243, s)-Nets in Base 3

(243−86, 243, 162)-Net over F₃ — Constructive and digital

Digital (157, 243, 162)-net over F₃, using

7 times m-reduction [i] based on digital (157, 250, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 125, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(243−86, 243, 315)-Net over F₃ — Digital

Digital (157, 243, 315)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−86, 243, 4152)-Net in Base 3 — Upper bound on s

There is no (157, 243, 4153)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 87 507991 560582 163010 101317 813702 776304 339964 572755 723607 038309 863826 039400 300718 878200 480776 988969 068310 905275 076635 > 3²⁴³ [i]