MinT - Best Known (60, 60+85, s)-Nets in Base 8

Best Known (60, 60+85, s)-Nets in Base 8

(60, 60+85, 98)-Net over F₈ — Constructive and digital

Digital (60, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(60, 60+85, 144)-Net over F₈ — Digital

Digital (60, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 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]

(60, 60+85, 2918)-Net in Base 8 — Upper bound on s

There is no (60, 145, 2919)-net in base 8, because

1 times m-reduction [i] would yield (60, 144, 2919)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11237 515812 033458 154789 680017 670820 346594 189268 202439 823972 405346 360116 924962 198211 771436 332062 048205 389104 397676 312750 859754 711240 > 8¹⁴⁴ [i]