MinT - Best Known (60, 60+81, s)-Nets in Base 8

Best Known (60, 60+81, s)-Nets in Base 8

(60, 60+81, 98)-Net over F₈ — Constructive and digital

Digital (60, 141, 98)-net over F₈, using

t-expansion [i] based on digital (37, 141, 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+81, 144)-Net over F₈ — Digital

Digital (60, 141, 144)-net over F₈, using

t-expansion [i] based on digital (45, 141, 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+81, 3237)-Net in Base 8 — Upper bound on s

There is no (60, 141, 3238)-net in base 8, because

1 times m-reduction [i] would yield (60, 140, 3238)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 740216 366345 513736 489803 722622 572389 414701 818433 333967 196392 687862 929854 089532 439195 785262 554733 164769 796406 850130 463837 186256 > 8¹⁴⁰ [i]