MinT - Best Known (111−65, 111, s)-Nets in Base 8

Best Known (111−65, 111, s)-Nets in Base 8

(111−65, 111, 98)-Net over F₈ — Constructive and digital

Digital (46, 111, 98)-net over F₈, using

t-expansion [i] based on digital (37, 111, 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]

(111−65, 111, 144)-Net over F₈ — Digital

Digital (46, 111, 144)-net over F₈, using

t-expansion [i] based on digital (45, 111, 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]

(111−65, 111, 2303)-Net in Base 8 — Upper bound on s

There is no (46, 111, 2304)-net in base 8, because

1 times m-reduction [i] would yield (46, 110, 2304)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2201 059219 792443 874084 972019 258631 025814 081509 858667 642591 556366 787357 385306 190775 527674 262250 410537 > 8¹¹⁰ [i]