MinT - Best Known (84−37, 84, s)-Nets in Base 8

Best Known (84−37, 84, s)-Nets in Base 8

(84−37, 84, 256)-Net over F₈ — Constructive and digital

Digital (47, 84, 256)-net over F₈, using

trace code for nets [i] based on digital (5, 42, 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]

(84−37, 84, 266)-Net over F₈ — Digital

Digital (47, 84, 266)-net over F₈, using

trace code for nets [i] based on digital (5, 42, 133)-net over F₆₄, using
- net from sequence [i] based on digital (5, 132)-sequence over F₆₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 133, using
    - a curve from the manYPoints database [i]

(84−37, 84, 15738)-Net in Base 8 — Upper bound on s

There is no (47, 84, 15739)-net in base 8, because

1 times m-reduction [i] would yield (47, 83, 15739)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 904 707077 552236 034147 312493 652588 644782 048131 055115 138700 448146 126008 966265 > 8⁸³ [i]