MinT - Best Known (205−70, 205, s)-Nets in Base 3

Best Known (205−70, 205, s)-Nets in Base 3

(205−70, 205, 162)-Net over F₃ — Constructive and digital

Digital (135, 205, 162)-net over F₃, using

1 times m-reduction [i] based on digital (135, 206, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 103, 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]

(205−70, 205, 302)-Net over F₃ — Digital

Digital (135, 205, 302)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(205−70, 205, 4298)-Net in Base 3 — Upper bound on s

There is no (135, 205, 4299)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 64 680676 011863 269624 815765 416077 304457 039151 581086 326424 813855 973476 756292 731092 140355 290913 548555 > 3²⁰⁵ [i]