MinT - Best Known (105, 105+55, s)-Nets in Base 3

Best Known (105, 105+55, s)-Nets in Base 3

(105, 105+55, 156)-Net over F₃ — Constructive and digital

Digital (105, 160, 156)-net over F₃, using

6 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+55, 240)-Net over F₃ — Digital

Digital (105, 160, 240)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(105, 105+55, 3498)-Net in Base 3 — Upper bound on s

There is no (105, 160, 3499)-net in base 3, because

1 times m-reduction [i] would yield (105, 159, 3499)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 7336 867700 711115 228263 437278 255380 998093 982832 869981 875882 461816 702620 004507 > 3¹⁵⁹ [i]