MinT - Best Known (145−98, 145, s)-Nets in Base 8

Best Known (145−98, 145, s)-Nets in Base 8

(145−98, 145, 98)-Net over F₈ — Constructive and digital

Digital (47, 145, 98)-net over F₈, using

t-expansion [i] based on digital (37, 145, 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]

(145−98, 145, 144)-Net over F₈ — Digital

Digital (47, 145, 144)-net over F₈, using

t-expansion [i] based on digital (45, 145, 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]

(145−98, 145, 1253)-Net in Base 8 — Upper bound on s

There is no (47, 145, 1254)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 90829 337560 203546 450947 658209 895424 199812 700715 365791 924982 635050 334574 937863 427155 891751 853938 054047 730669 583769 549310 613420 286844 > 8¹⁴⁵ [i]