MinT - Best Known (169−122, 169, s)-Nets in Base 8

Best Known (169−122, 169, s)-Nets in Base 8

(169−122, 169, 98)-Net over F₈ — Constructive and digital

Digital (47, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(169−122, 169, 144)-Net over F₈ — Digital

Digital (47, 169, 144)-net over F₈, using

t-expansion [i] based on digital (45, 169, 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]

(169−122, 169, 1031)-Net in Base 8 — Upper bound on s

There is no (47, 169, 1032)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 441 805540 851940 094438 059014 833149 291727 937732 621466 675250 022885 972902 295858 157099 983633 752041 515264 155725 391863 577580 117841 923768 406954 895171 843544 448640 > 8¹⁶⁹ [i]