MinT - Best Known (76, 76+74, s)-Nets in Base 8

Best Known (76, 76+74, s)-Nets in Base 8

(76, 76+74, 160)-Net over F₈ — Constructive and digital

Digital (76, 150, 160)-net over F₈, using

trace code for nets [i] based on digital (1, 75, 80)-net over F₆₄, using
- net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
    - a function field by SÃ©mirat [i]

(76, 76+74, 257)-Net over F₈ — Digital

Digital (76, 150, 257)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(76, 76+74, 9570)-Net in Base 8 — Upper bound on s

There is no (76, 150, 9571)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2912 927401 355176 630788 533780 974251 456731 282584 970532 032934 413517 014571 146037 518166 845226 428026 328705 512679 479973 519173 007392 719938 539488 > 8¹⁵⁰ [i]