MinT - Best Known (197−55, 197, s)-Nets in Base 3

Best Known (197−55, 197, s)-Nets in Base 3

(197−55, 197, 282)-Net over F₃ — Constructive and digital

Digital (142, 197, 282)-net over F₃, using

1 times m-reduction [i] based on digital (142, 198, 282)-net over F₃, using
- trace code for nets [i] based on digital (10, 66, 94)-net over F₂₇, using
  - net from sequence [i] based on digital (10, 93)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 10 and N(F) ≥ 94, using
      - a function field by SÃ©mirat [i]

(197−55, 197, 556)-Net over F₃ — Digital

Digital (142, 197, 556)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(197−55, 197, 15856)-Net in Base 3 — Upper bound on s

There is no (142, 197, 15857)-net in base 3, because

1 times m-reduction [i] would yield (142, 196, 15857)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3283 681741 069596 606940 271563 207658 589534 093542 347887 832556 374606 516479 705311 028160 336622 462971 > 3¹⁹⁶ [i]