MinT - Best Known (193−49, 193, s)-Nets in Base 3

Best Known (193−49, 193, s)-Nets in Base 3

(193−49, 193, 288)-Net over F₃ — Constructive and digital

Digital (144, 193, 288)-net over F₃, using

t-expansion [i] based on digital (143, 193, 288)-net over F₃, using
- 5 times m-reduction [i] based on digital (143, 198, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 66, 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]

(193−49, 193, 777)-Net over F₃ — Digital

Digital (144, 193, 777)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−49, 193, 32135)-Net in Base 3 — Upper bound on s

There is no (144, 193, 32136)-net in base 3, because

1 times m-reduction [i] would yield (144, 192, 32136)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 498115 020485 831362 520184 723983 053239 815413 368541 831135 605793 604949 262211 769522 134015 481089 > 3¹⁹² [i]