MinT - Best Known (250−91, 250, s)-Nets in Base 3

Best Known (250−91, 250, s)-Nets in Base 3

(250−91, 250, 162)-Net over F₃ — Constructive and digital

Digital (159, 250, 162)-net over F₃, using

t-expansion [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]

(250−91, 250, 298)-Net over F₃ — Digital

Digital (159, 250, 298)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(250−91, 250, 3803)-Net in Base 3 — Upper bound on s

There is no (159, 250, 3804)-net in base 3, because

1 times m-reduction [i] would yield (159, 249, 3804)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63910 342041 360193 417536 380364 346528 095396 831345 967910 601721 083143 074176 729406 482293 449333 024469 826187 231308 098297 907097 > 3²⁴⁹ [i]