MinT - Best Known (131, 196, s)-Nets in Base 3

Best Known (131, 196, s)-Nets in Base 3

(131, 196, 162)-Net over F₃ — Constructive and digital

Digital (131, 196, 162)-net over F₃, using

2 times m-reduction [i] based on digital (131, 198, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 99, 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]

(131, 196, 318)-Net over F₃ — Digital

Digital (131, 196, 318)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 196, 5136)-Net in Base 3 — Upper bound on s

There is no (131, 196, 5137)-net in base 3, because

1 times m-reduction [i] would yield (131, 195, 5137)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1097 078762 339252 234453 957694 257783 393082 445767 206812 974312 972527 837789 413678 664925 501822 592641 > 3¹⁹⁵ [i]