MinT - Best Known (102, 156, s)-Nets in Base 3

Best Known (102, 156, s)-Nets in Base 3

(102, 156, 156)-Net over F₃ — Constructive and digital

Digital (102, 156, 156)-net over F₃, using

4 times m-reduction [i] based on digital (102, 160, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 80, 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]

(102, 156, 230)-Net over F₃ — Digital

Digital (102, 156, 230)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 156, 3093)-Net in Base 3 — Upper bound on s

There is no (102, 156, 3094)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 271 974550 980966 357291 981279 381123 306398 923855 507295 125274 153029 354033 700913 > 3¹⁵⁶ [i]