MinT - Best Known (150, 198, s)-Nets in Base 3

Best Known (150, 198, s)-Nets in Base 3

(150, 198, 400)-Net over F₃ — Constructive and digital

Digital (150, 198, 400)-net over F₃, using

3² times duplication [i] based on digital (148, 196, 400)-net over F₃, using
- trace code for nets [i] based on digital (1, 49, 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]

(150, 198, 954)-Net over F₃ — Digital

Digital (150, 198, 954)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(150, 198, 42300)-Net in Base 3 — Upper bound on s

There is no (150, 198, 42301)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 29526 838798 809387 187256 691541 225036 567970 243219 155999 581730 268367 053595 325359 718951 434823 550241 > 3¹⁹⁸ [i]