MinT - Best Known (44, 44+105, s)-Nets in Base 8

Best Known (44, 44+105, s)-Nets in Base 8

(44, 44+105, 98)-Net over F₈ — Constructive and digital

Digital (44, 149, 98)-net over F₈, using

t-expansion [i] based on digital (37, 149, 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]

(44, 44+105, 130)-Net over F₈ — Digital

Digital (44, 149, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(44, 44+105, 1041)-Net in Base 8 — Upper bound on s

There is no (44, 149, 1042)-net in base 8, because

1 times m-reduction [i] would yield (44, 148, 1042)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46 114364 066546 184753 365401 863774 384333 651179 715219 623195 170810 194991 520276 498715 025776 156181 054341 853278 819340 440104 499348 461109 657856 > 8¹⁴⁸ [i]