MinT - Best Known (225−79, 225, s)-Nets in Base 3

Best Known (225−79, 225, s)-Nets in Base 3

(225−79, 225, 162)-Net over F₃ — Constructive and digital

Digital (146, 225, 162)-net over F₃, using

3 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]

(225−79, 225, 301)-Net over F₃ — Digital

Digital (146, 225, 301)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(225−79, 225, 4195)-Net in Base 3 — Upper bound on s

There is no (146, 225, 4196)-net in base 3, because

1 times m-reduction [i] would yield (146, 224, 4196)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 75038 876711 606350 360259 810139 757511 132506 238374 996166 484625 878122 128269 689527 074109 506835 058296 832378 132337 > 3²²⁴ [i]