MinT - Best Known (59, 59+87, s)-Nets in Base 8

Best Known (59, 59+87, s)-Nets in Base 8

(59, 59+87, 98)-Net over F₈ — Constructive and digital

Digital (59, 146, 98)-net over F₈, using

t-expansion [i] based on digital (37, 146, 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]

(59, 59+87, 144)-Net over F₈ — Digital

Digital (59, 146, 144)-net over F₈, using

t-expansion [i] based on digital (45, 146, 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]

(59, 59+87, 2650)-Net in Base 8 — Upper bound on s

There is no (59, 146, 2651)-net in base 8, because

1 times m-reduction [i] would yield (59, 145, 2651)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 90019 785657 467372 792815 219607 558428 276828 884506 561184 161761 995390 328085 933543 388647 747980 401138 501247 507061 820950 033056 069019 054640 > 8¹⁴⁵ [i]