MinT - Best Known (105, 105+57, s)-Nets in Base 3

Best Known (105, 105+57, s)-Nets in Base 3

(105, 105+57, 156)-Net over F₃ — Constructive and digital

Digital (105, 162, 156)-net over F₃, using

4 times m-reduction [i] based on digital (105, 166, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 83, 78)-net over F₉, using
  - net from sequence [i] based on digital (22, 77)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
      - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(105, 105+57, 226)-Net over F₃ — Digital

Digital (105, 162, 226)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+57, 3101)-Net in Base 3 — Upper bound on s

There is no (105, 162, 3102)-net in base 3, because

1 times m-reduction [i] would yield (105, 161, 3102)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 65706 332217 289367 930940 950631 839849 643815 204630 101947 952882 239552 416537 611641 > 3¹⁶¹ [i]