MinT - Best Known (74, 138, s)-Nets in Base 8

Best Known (74, 138, s)-Nets in Base 8

(74, 138, 256)-Net over F₈ — Constructive and digital

Digital (74, 138, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 69, 128)-net over F₆₄, using
- net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
    - a function field by SÃ©mirat [i]

(74, 138, 311)-Net over F₈ — Digital

Digital (74, 138, 311)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(74, 138, 14313)-Net in Base 8 — Upper bound on s

There is no (74, 138, 14314)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 42343 157015 931820 765025 790139 141791 412279 884720 822019 999990 844039 766475 621082 908615 963739 029504 163870 474400 403417 269292 083303 > 8¹³⁸ [i]