MinT - Best Known (60, 60+95, s)-Nets in Base 8

Best Known (60, 60+95, s)-Nets in Base 8

(60, 60+95, 98)-Net over F₈ — Constructive and digital

Digital (60, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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+95, 144)-Net over F₈ — Digital

Digital (60, 155, 144)-net over F₈, using

t-expansion [i] based on digital (45, 155, 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+95, 2358)-Net in Base 8 — Upper bound on s

There is no (60, 155, 2359)-net in base 8, because

1 times m-reduction [i] would yield (60, 154, 2359)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 014413 137101 972316 821132 754482 770078 725869 553659 974883 451112 190513 820348 089942 599388 062077 801336 608909 623883 490701 121725 733865 697253 691264 > 8¹⁵⁴ [i]