MinT - Best Known (44, 44+49, s)-Nets in Base 8

Best Known (44, 44+49, s)-Nets in Base 8

(44, 44+49, 98)-Net over F₈ — Constructive and digital

Digital (44, 93, 98)-net over F₈, using

t-expansion [i] based on digital (37, 93, 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+49, 133)-Net over F₈ — Digital

Digital (44, 93, 133)-net over F₈, using

Gilbertâ€“VarÅ¡amov bound [i]

(44, 44+49, 4041)-Net in Base 8 — Upper bound on s

There is no (44, 93, 4042)-net in base 8, because

1 times m-reduction [i] would yield (44, 92, 4042)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 121994 518970 071677 073232 257073 599245 787697 982151 983167 227779 998459 154374 550511 615516 > 8⁹² [i]