MinT - Best Known (124−71, 124, s)-Nets in Base 8

Best Known (124−71, 124, s)-Nets in Base 8

(124−71, 124, 98)-Net over F₈ — Constructive and digital

Digital (53, 124, 98)-net over F₈, using

t-expansion [i] based on digital (37, 124, 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]

(124−71, 124, 144)-Net over F₈ — Digital

Digital (53, 124, 144)-net over F₈, using

t-expansion [i] based on digital (45, 124, 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]

(124−71, 124, 2942)-Net in Base 8 — Upper bound on s

There is no (53, 124, 2943)-net in base 8, because

1 times m-reduction [i] would yield (53, 123, 2943)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1215 647937 199153 758449 308030 706704 040786 143432 758468 618601 226764 299260 089075 215501 296426 158100 762841 437201 913884 > 8¹²³ [i]