MinT - Best Known (78, 78+39, s)-Nets in Base 3

Best Known (78, 78+39, s)-Nets in Base 3

(78, 78+39, 148)-Net over F₃ — Constructive and digital

Digital (78, 117, 148)-net over F₃, using

5 times m-reduction [i] based on digital (78, 122, 148)-net over F₃, using
- trace code for nets [i] based on digital (17, 61, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(78, 78+39, 204)-Net over F₃ — Digital

Digital (78, 117, 204)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+39, 3225)-Net in Base 3 — Upper bound on s

There is no (78, 117, 3226)-net in base 3, because

1 times m-reduction [i] would yield (78, 116, 3226)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 22 190707 344513 120164 225395 566149 859071 165062 930244 059857 > 3¹¹⁶ [i]