MinT - Best Known (148, 148+43, s)-Nets in Base 3

Best Known (148, 148+43, s)-Nets in Base 3

(148, 148+43, 600)-Net over F₃ — Constructive and digital

Digital (148, 191, 600)-net over F₃, using

1 times m-reduction [i] based on digital (148, 192, 600)-net over F₃, using
- trace code for nets [i] based on digital (4, 48, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(148, 148+43, 1241)-Net over F₃ — Digital

Digital (148, 191, 1241)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+43, 89986)-Net in Base 3 — Upper bound on s

There is no (148, 191, 89987)-net in base 3, because

1 times m-reduction [i] would yield (148, 190, 89987)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 499232 968191 924670 257566 281710 351033 261435 638148 004676 284481 833383 982983 150048 033037 508575 > 3¹⁹⁰ [i]