MinT - Best Known (175−38, 175, s)-Nets in Base 3

Best Known (175−38, 175, s)-Nets in Base 3

(175−38, 175, 640)-Net over F₃ — Constructive and digital

Digital (137, 175, 640)-net over F₃, using

1 times m-reduction [i] based on digital (137, 176, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 44, 160)-net over F₈₁, using
  - net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
      - a function field by SÃ©mirat [i]

(175−38, 175, 1341)-Net over F₃ — Digital

Digital (137, 175, 1341)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(175−38, 175, 98319)-Net in Base 3 — Upper bound on s

There is no (137, 175, 98320)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 313489 634202 972106 217469 213637 968685 688711 576867 201974 348169 011570 328395 151965 204545 > 3¹⁷⁵ [i]