MinT - Best Known (176, 232, s)-Nets in Base 3

Best Known (176, 232, s)-Nets in Base 3

(176, 232, 464)-Net over F₃ — Constructive and digital

Digital (176, 232, 464)-net over F₃, using

trace code for nets [i] based on digital (2, 58, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(176, 232, 1105)-Net over F₃ — Digital

Digital (176, 232, 1105)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(176, 232, 50702)-Net in Base 3 — Upper bound on s

There is no (176, 232, 50703)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 492 304221 602617 385359 310734 894470 588166 946822 126568 389151 501035 774760 904652 855313 309154 008393 276951 509330 311369 > 3²³² [i]