MinT - Best Known (191−51, 191, s)-Nets in Base 3

Best Known (191−51, 191, s)-Nets in Base 3

(191−51, 191, 288)-Net over F₃ — Constructive and digital

Digital (140, 191, 288)-net over F₃, using

t-expansion [i] based on digital (139, 191, 288)-net over F₃, using
- 1 times m-reduction [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]

(191−51, 191, 636)-Net over F₃ — Digital

Digital (140, 191, 636)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(191−51, 191, 21489)-Net in Base 3 — Upper bound on s

There is no (140, 191, 21490)-net in base 3, because

1 times m-reduction [i] would yield (140, 190, 21490)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 501733 337131 576106 569759 064055 824926 255164 437188 150812 218951 763975 208608 292459 809607 860341 > 3¹⁹⁰ [i]