MinT - Best Known (78, 142, s)-Nets in Base 8

Best Known (78, 142, s)-Nets in Base 8

(78, 142, 354)-Net over F₈ — Constructive and digital

Digital (78, 142, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 71, 177)-net over F₆₄, using
- net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
    - a function field by GarcÃa and Quoos [i]

(78, 142, 358)-Net over F₈ — Digital

Digital (78, 142, 358)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 142, 18568)-Net in Base 8 — Upper bound on s

There is no (78, 142, 18569)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 173 462995 904400 254722 906653 792127 952018 003522 514510 252791 679556 966458 397002 926719 058156 627487 401680 391109 979317 985263 346255 513196 > 8¹⁴² [i]