MinT - Best Known (183, 250, s)-Nets in Base 3

Best Known (183, 250, s)-Nets in Base 3

(183, 250, 288)-Net over F₃ — Constructive and digital

Digital (183, 250, 288)-net over F₃, using

3¹ times duplication [i] based on digital (182, 249, 288)-net over F₃, using
- t-expansion [i] based on digital (177, 249, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 83, 96)-net over F₂₇, using
    - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
        an explicitly constructive algebraic function field [i]

(183, 250, 789)-Net over F₃ — Digital

Digital (183, 250, 789)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(183, 250, 26174)-Net in Base 3 — Upper bound on s

There is no (183, 250, 26175)-net in base 3, because

1 times m-reduction [i] would yield (183, 249, 26175)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63582 790605 715650 086318 927091 405770 791041 103357 452797 559801 644571 083853 643087 646461 355162 889110 601206 637895 826724 375615 > 3²⁴⁹ [i]