MinT - Best Known (173−127, 173, s)-Nets in Base 8

Best Known (173−127, 173, s)-Nets in Base 8

(173−127, 173, 98)-Net over F₈ — Constructive and digital

Digital (46, 173, 98)-net over F₈, using

t-expansion [i] based on digital (37, 173, 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]

(173−127, 173, 144)-Net over F₈ — Digital

Digital (46, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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]

(173−127, 173, 974)-Net in Base 8 — Upper bound on s

There is no (46, 173, 975)-net in base 8, because

1 times m-reduction [i] would yield (46, 172, 975)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 218093 722434 605463 633690 749119 666430 430730 319162 440231 437641 422970 653853 996561 205570 701288 447654 904582 675044 881701 722584 300760 968687 633690 052829 039788 596832 > 8¹⁷² [i]