MinT - Best Known (169, 243, s)-Nets in Base 4

Best Known (169, 243, s)-Nets in Base 4

(169, 243, 531)-Net over F₄ — Constructive and digital

Digital (169, 243, 531)-net over F₄, using

trace code for nets [i] based on digital (7, 81, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(169, 243, 923)-Net over F₄ — Digital

Digital (169, 243, 923)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(169, 243, 43909)-Net in Base 4 — Upper bound on s

There is no (169, 243, 43910)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 199 843699 202148 832286 982820 563846 332014 426610 422994 397917 879326 573511 970532 748456 087099 426278 835175 524296 142087 507969 533969 654488 385545 792312 610300 > 4²⁴³ [i]