MinT - Best Known (249−76, 249, s)-Nets in Base 3

Best Known (249−76, 249, s)-Nets in Base 3

(249−76, 249, 246)-Net over F₃ — Constructive and digital

Digital (173, 249, 246)-net over F₃, using

trace code for nets [i] based on digital (7, 83, 82)-net over F₂₇, using
- net from sequence [i] based on digital (7, 81)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 7 and N(F) ≥ 82, using
    - a function field by SÃ©mirat [i]

(249−76, 249, 509)-Net over F₃ — Digital

Digital (173, 249, 509)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(249−76, 249, 10012)-Net in Base 3 — Upper bound on s

There is no (173, 249, 10013)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 63628 983636 084867 560099 759766 419208 071824 673949 242734 687245 843607 243132 974643 730258 050184 924956 518682 700838 516810 050481 > 3²⁴⁹ [i]