MinT - Best Known (115−69, 115, s)-Nets in Base 8

Best Known (115−69, 115, s)-Nets in Base 8

(115−69, 115, 98)-Net over F₈ — Constructive and digital

Digital (46, 115, 98)-net over F₈, using

t-expansion [i] based on digital (37, 115, 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]

(115−69, 115, 144)-Net over F₈ — Digital

Digital (46, 115, 144)-net over F₈, using

t-expansion [i] based on digital (45, 115, 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]

(115−69, 115, 2041)-Net in Base 8 — Upper bound on s

There is no (46, 115, 2042)-net in base 8, because

1 times m-reduction [i] would yield (46, 114, 2042)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9 082722 448384 691795 023566 986723 119161 308093 785201 631153 274775 816880 209334 833292 617273 889800 878207 581340 > 8¹¹⁴ [i]