MinT - Best Known (131, 131+67, s)-Nets in Base 3

Best Known (131, 131+67, s)-Nets in Base 3

(131, 131+67, 162)-Net over F₃ — Constructive and digital

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, 131+67, 301)-Net over F₃ — Digital

Digital (131, 198, 301)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(131, 131+67, 4608)-Net in Base 3 — Upper bound on s

There is no (131, 198, 4609)-net in base 3, because

1 times m-reduction [i] would yield (131, 197, 4609)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 9879 556274 870765 707794 199680 198970 967428 633958 516835 038378 444925 244935 291866 896477 483417 886595 > 3¹⁹⁷ [i]