MinT - Best Known (51, 51+37, s)-Nets in Base 8

Best Known (51, 51+37, s)-Nets in Base 8

(51, 51+37, 354)-Net over F₈ — Constructive and digital

Digital (51, 88, 354)-net over F₈, using

trace code for nets [i] based on digital (7, 44, 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]

(51, 51+37, 24990)-Net in Base 8 — Upper bound on s

There is no (51, 88, 24991)-net in base 8, because

1 times m-reduction [i] would yield (51, 87, 24991)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 706730 980612 497775 284472 966986 776781 106061 923823 022346 620307 736240 489681 679905 > 8⁸⁷ [i]