MinT - Best Known (249−66, 249, s)-Nets in Base 3

Best Known (249−66, 249, s)-Nets in Base 3

(249−66, 249, 288)-Net over F₃ — Constructive and digital

Digital (183, 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]

(249−66, 249, 818)-Net over F₃ — Digital

Digital (183, 249, 818)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−66, 249, 26174)-Net in Base 3 — Upper bound on s

There is no (183, 249, 26175)-net in base 3, because

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]