MinT - Best Known (78, 78+65, s)-Nets in Base 8

Best Known (78, 78+65, s)-Nets in Base 8

(78, 78+65, 256)-Net over F₈ — Constructive and digital

Digital (78, 143, 256)-net over F₈, using

3 times m-reduction [i] based on digital (78, 146, 256)-net over F₈, using
- trace code for nets [i] based on digital (5, 73, 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]

(78, 78+65, 348)-Net over F₈ — Digital

Digital (78, 143, 348)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(78, 78+65, 18568)-Net in Base 8 — Upper bound on s

There is no (78, 143, 18569)-net in base 8, because

1 times m-reduction [i] would yield (78, 142, 18569)-net in base 8, but
- 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]