MinT - Best Known (249−59, 249, s)-Nets in Base 3

Best Known (249−59, 249, s)-Nets in Base 3

(249−59, 249, 464)-Net over F₃ — Constructive and digital

Digital (190, 249, 464)-net over F₃, using

3¹ times duplication [i] based on digital (189, 248, 464)-net over F₃, using
- t-expansion [i] based on digital (188, 248, 464)-net over F₃, using
  - trace code for nets [i] based on digital (2, 62, 116)-net over F₈₁, using
    - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
        a function field by SÃ©mirat [i]

(249−59, 249, 1264)-Net over F₃ — Digital

Digital (190, 249, 1264)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−59, 249, 70165)-Net in Base 3 — Upper bound on s

There is no (190, 249, 70166)-net in base 3, because

1 times m-reduction [i] would yield (190, 248, 70166)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21189 448228 066529 654471 497283 116165 625041 166478 102118 187168 284582 425329 225411 889678 921462 956754 008876 656173 101246 451285 > 3²⁴⁸ [i]