MinT - Best Known (102, 153, s)-Nets in Base 3

Best Known (102, 153, s)-Nets in Base 3

(102, 153, 156)-Net over F₃ — Constructive and digital

Digital (102, 153, 156)-net over F₃, using

7 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, 153, 255)-Net over F₃ — Digital

Digital (102, 153, 255)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(102, 153, 4025)-Net in Base 3 — Upper bound on s

There is no (102, 153, 4026)-net in base 3, because

1 times m-reduction [i] would yield (102, 152, 4026)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 3 331613 228651 920259 763712 036582 348604 746265 736124 393326 342611 263080 394245 > 3¹⁵² [i]