MinT - Best Known (44, 44+129, s)-Nets in Base 8

Best Known (44, 44+129, s)-Nets in Base 8

(44, 44+129, 98)-Net over F₈ — Constructive and digital

Digital (44, 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]

(44, 44+129, 130)-Net over F₈ — Digital

Digital (44, 173, 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+129, 902)-Net in Base 8 — Upper bound on s

There is no (44, 173, 903)-net in base 8, because

1 times m-reduction [i] would yield (44, 172, 903)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 226576 017496 315988 504286 880694 888269 973169 537859 272724 582955 909952 380804 917855 729470 053575 965613 193993 318667 390184 311622 330617 993396 499983 152810 172336 518106 > 8¹⁷² [i]