MinT - Best Known (249−61, 249, s)-Nets in Base 3

Best Known (249−61, 249, s)-Nets in Base 3

(249−61, 249, 400)-Net over F₃ — Constructive and digital

Digital (188, 249, 400)-net over F₃, using

3¹ times duplication [i] based on digital (187, 248, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 62, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]

(249−61, 249, 1104)-Net over F₃ — Digital

Digital (188, 249, 1104)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−61, 249, 52932)-Net in Base 3 — Upper bound on s

There is no (188, 249, 52933)-net in base 3, because

1 times m-reduction [i] would yield (188, 248, 52933)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21197 879371 863423 970297 503846 295494 074199 689385 445941 426475 618235 155507 363719 591357 179617 412937 184370 040954 598119 273505 > 3²⁴⁸ [i]