MinT - Best Known (193−53, 193, s)-Nets in Base 3

Best Known (193−53, 193, s)-Nets in Base 3

(193−53, 193, 288)-Net over F₃ — Constructive and digital

Digital (140, 193, 288)-net over F₃, using

3¹ times duplication [i] based on digital (139, 192, 288)-net over F₃, using
- trace code for nets [i] based on digital (11, 64, 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]

(193−53, 193, 580)-Net over F₃ — Digital

Digital (140, 193, 580)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(193−53, 193, 17578)-Net in Base 3 — Upper bound on s

There is no (140, 193, 17579)-net in base 3, because

1 times m-reduction [i] would yield (140, 192, 17579)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 40 491794 896883 078966 280856 860267 437524 718795 754948 098138 807213 913609 521841 307085 555126 768901 > 3¹⁹² [i]