MinT - Best Known (245−89, 245, s)-Nets in Base 3

Best Known (245−89, 245, s)-Nets in Base 3

(245−89, 245, 162)-Net over F₃ — Constructive and digital

Digital (156, 245, 162)-net over F₃, using

3 times m-reduction [i] based on digital (156, 248, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 124, 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]

(245−89, 245, 295)-Net over F₃ — Digital

Digital (156, 245, 295)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(245−89, 245, 3773)-Net in Base 3 — Upper bound on s

There is no (156, 245, 3774)-net in base 3, because

1 times m-reduction [i] would yield (156, 244, 3774)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 261 799674 958930 976981 889472 445012 609391 597803 376539 484672 073920 827774 180660 726182 754870 855052 430261 624131 351785 014809 > 3²⁴⁴ [i]