MinT - Best Known (223−77, 223, s)-Nets in Base 3

Best Known (223−77, 223, s)-Nets in Base 3

(223−77, 223, 162)-Net over F₃ — Constructive and digital

Digital (146, 223, 162)-net over F₃, using

5 times m-reduction [i] based on digital (146, 228, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 114, 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]

(223−77, 223, 314)-Net over F₃ — Digital

Digital (146, 223, 314)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(223−77, 223, 4566)-Net in Base 3 — Upper bound on s

There is no (146, 223, 4567)-net in base 3, because

1 times m-reduction [i] would yield (146, 222, 4567)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8338 700846 321297 603374 466582 264128 172349 957400 883348 301765 401488 425127 991619 154684 202100 993452 269214 506149 > 3²²² [i]