MinT - Best Known (59, 169, s)-Nets in Base 8

Best Known (59, 169, s)-Nets in Base 8

(59, 169, 98)-Net over F₈ — Constructive and digital

Digital (59, 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]

(59, 169, 144)-Net over F₈ — Digital

Digital (59, 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]

(59, 169, 1780)-Net in Base 8 — Upper bound on s

There is no (59, 169, 1781)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 420 296623 889309 171177 370990 454869 334210 255733 774553 540879 433950 876917 478055 003640 670532 033066 094891 235313 401022 776306 121395 222402 584674 093894 561002 187200 > 8¹⁶⁹ [i]