MinT - Best Known (149−41, 149, s)-Nets in Base 3

Best Known (149−41, 149, s)-Nets in Base 3

(149−41, 149, 252)-Net over F₃ — Constructive and digital

Digital (108, 149, 252)-net over F₃, using

1 times m-reduction [i] based on digital (108, 150, 252)-net over F₃, using
- trace code for nets [i] based on digital (8, 50, 84)-net over F₂₇, using
  - net from sequence [i] based on digital (8, 83)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 84, using
      - a function field by SÃ©mirat [i]

(149−41, 149, 466)-Net over F₃ — Digital

Digital (108, 149, 466)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(149−41, 149, 14072)-Net in Base 3 — Upper bound on s

There is no (108, 149, 14073)-net in base 3, because

1 times m-reduction [i] would yield (108, 148, 14073)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 41136 677509 033504 923028 394716 894849 569584 129301 300302 727349 105361 416401 > 3¹⁴⁸ [i]