MinT - Best Known (241−83, 241, s)-Nets in Base 3

Best Known (241−83, 241, s)-Nets in Base 3

(241−83, 241, 162)-Net over F₃ — Constructive and digital

Digital (158, 241, 162)-net over F₃, using

t-expansion [i] based on digital (157, 241, 162)-net over F₃, using
- 9 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]

(241−83, 241, 339)-Net over F₃ — Digital

Digital (158, 241, 339)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(241−83, 241, 4969)-Net in Base 3 — Upper bound on s

There is no (158, 241, 4970)-net in base 3, because

1 times m-reduction [i] would yield (158, 240, 4970)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 254175 752138 545871 958858 031819 862865 653458 722940 104060 982677 488399 648173 135177 923480 143584 296334 575983 117550 447045 > 3²⁴⁰ [i]