MinT - Best Known (149, 149+42, s)-Nets in Base 3

Best Known (149, 149+42, s)-Nets in Base 3

(149, 149+42, 640)-Net over F₃ — Constructive and digital

Digital (149, 191, 640)-net over F₃, using

1 times m-reduction [i] based on digital (149, 192, 640)-net over F₃, using
- trace code for nets [i] based on digital (5, 48, 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]

(149, 149+42, 1368)-Net over F₃ — Digital

Digital (149, 191, 1368)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149, 149+42, 94820)-Net in Base 3 — Upper bound on s

There is no (149, 191, 94821)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 13 497474 486031 453708 779757 647206 244245 269178 528115 877022 907999 276401 793874 029222 230259 645083 > 3¹⁹¹ [i]