MinT - Best Known (237−94, 237, s)-Nets in Base 3

Best Known (237−94, 237, s)-Nets in Base 3

(237−94, 237, 156)-Net over F₃ — Constructive and digital

Digital (143, 237, 156)-net over F₃, using

5 times m-reduction [i] based on digital (143, 242, 156)-net over F₃, using
- trace code for nets [i] based on digital (22, 121, 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]

(237−94, 237, 222)-Net over F₃ — Digital

Digital (143, 237, 222)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(237−94, 237, 2292)-Net in Base 3 — Upper bound on s

There is no (143, 237, 2293)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 120558 017039 961685 688534 349608 282298 341407 083526 576495 534056 634178 116719 245727 401207 804968 840300 136694 973433 228475 > 3²³⁷ [i]