MinT - Best Known (63, 63+87, s)-Nets in Base 8

Best Known (63, 63+87, s)-Nets in Base 8

(63, 63+87, 98)-Net over F₈ — Constructive and digital

Digital (63, 150, 98)-net over F₈, using

t-expansion [i] based on digital (37, 150, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(63, 63+87, 144)-Net over F₈ — Digital

Digital (63, 150, 144)-net over F₈, using

t-expansion [i] based on digital (45, 150, 144)-net over F₈, using
- net from sequence [i] based on digital (45, 143)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 45 and N(F) ≥ 144, using
    - Drinfeld modules of rank 1 [i]

(63, 63+87, 3221)-Net in Base 8 — Upper bound on s

There is no (63, 150, 3222)-net in base 8, because

1 times m-reduction [i] would yield (63, 149, 3222)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 366 211620 724122 295721 692953 534906 403469 780968 677511 675548 687987 633153 673562 854430 789363 330480 340916 340176 186327 603622 302576 646447 670704 > 8¹⁴⁹ [i]