MinT - Best Known (232−80, 232, s)-Nets in Base 3

Best Known (232−80, 232, s)-Nets in Base 3

(232−80, 232, 162)-Net over F₃ — Constructive and digital

Digital (152, 232, 162)-net over F₃, using

8 times m-reduction [i] based on digital (152, 240, 162)-net over F₃, using
- trace code for nets [i] based on digital (32, 120, 81)-net over F₉, using
  - net from sequence [i] based on digital (32, 80)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
      - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(232−80, 232, 326)-Net over F₃ — Digital

Digital (152, 232, 326)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(232−80, 232, 4574)-Net in Base 3 — Upper bound on s

There is no (152, 232, 4575)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 494 324044 909797 177958 882450 321669 507739 259323 386661 844299 054166 915606 341864 553933 783151 678399 250194 592076 944817 > 3²³² [i]