MinT - Best Known (161, 242, s)-Nets in Base 3

Best Known (161, 242, s)-Nets in Base 3

(161, 242, 162)-Net over F₃ — Constructive and digital

Digital (161, 242, 162)-net over F₃, using

t-expansion [i] based on digital (157, 242, 162)-net over F₃, using
- 8 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]

(161, 242, 371)-Net over F₃ — Digital

Digital (161, 242, 371)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(161, 242, 5868)-Net in Base 3 — Upper bound on s

There is no (161, 242, 5869)-net in base 3, because

1 times m-reduction [i] would yield (161, 241, 5869)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9 734672 119529 329993 023359 111027 875547 229772 794377 656682 969227 515350 280757 720285 622338 460040 253456 144876 170145 428705 > 3²⁴¹ [i]