MinT - Best Known (178−66, 178, s)-Nets in Base 3

Best Known (178−66, 178, s)-Nets in Base 3

(178−66, 178, 156)-Net over F₃ — Constructive and digital

Digital (112, 178, 156)-net over F₃, using

2 times m-reduction [i] based on digital (112, 180, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 90, 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]

(178−66, 178, 210)-Net over F₃ — Digital

Digital (112, 178, 210)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(178−66, 178, 2433)-Net in Base 3 — Upper bound on s

There is no (112, 178, 2434)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 8 569372 918214 186352 148066 084300 342306 110124 986956 276433 755598 350035 924183 218568 653765 > 3¹⁷⁸ [i]