MinT - Best Known (195−49, 195, s)-Nets in Base 3

Best Known (195−49, 195, s)-Nets in Base 3

(195−49, 195, 288)-Net over F₃ — Constructive and digital

Digital (146, 195, 288)-net over F₃, using

t-expansion [i] based on digital (145, 195, 288)-net over F₃, using
- 6 times m-reduction [i] based on digital (145, 201, 288)-net over F₃, using
  - trace code for nets [i] based on digital (11, 67, 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]

(195−49, 195, 816)-Net over F₃ — Digital

Digital (146, 195, 816)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(195−49, 195, 35218)-Net in Base 3 — Upper bound on s

There is no (146, 195, 35219)-net in base 3, because

1 times m-reduction [i] would yield (146, 194, 35219)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 364 429302 866060 093348 350730 588304 945842 567802 865442 866407 923867 901048 439905 966287 837019 117009 > 3¹⁹⁴ [i]