MinT - Best Known (248−58, 248, s)-Nets in Base 3

Best Known (248−58, 248, s)-Nets in Base 3

(248−58, 248, 600)-Net over F₃ — Constructive and digital

Digital (190, 248, 600)-net over F₃, using

trace code for nets [i] based on digital (4, 62, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(248−58, 248, 1331)-Net over F₃ — Digital

Digital (190, 248, 1331)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(248−58, 248, 70165)-Net in Base 3 — Upper bound on s

There is no (190, 248, 70166)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 21189 448228 066529 654471 497283 116165 625041 166478 102118 187168 284582 425329 225411 889678 921462 956754 008876 656173 101246 451285 > 3²⁴⁸ [i]