MinT - Best Known (221−77, 221, s)-Nets in Base 3

Best Known (221−77, 221, s)-Nets in Base 3

(221−77, 221, 162)-Net over F₃ — Constructive and digital

Digital (144, 221, 162)-net over F₃, using

3 times m-reduction [i] based on digital (144, 224, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 112, 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]

(221−77, 221, 303)-Net over F₃ — Digital

Digital (144, 221, 303)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(221−77, 221, 4308)-Net in Base 3 — Upper bound on s

There is no (144, 221, 4309)-net in base 3, because

1 times m-reduction [i] would yield (144, 220, 4309)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 932 001801 456691 788455 679186 076919 945479 963213 604960 149315 981446 464709 419966 817613 797188 558125 211269 225185 > 3²²⁰ [i]