MinT - Best Known (141−82, 141, s)-Nets in Base 8

Best Known (141−82, 141, s)-Nets in Base 8

(141−82, 141, 98)-Net over F₈ — Constructive and digital

Digital (59, 141, 98)-net over F₈, using

t-expansion [i] based on digital (37, 141, 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]

(141−82, 141, 144)-Net over F₈ — Digital

Digital (59, 141, 144)-net over F₈, using

t-expansion [i] based on digital (45, 141, 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]

(141−82, 141, 2915)-Net in Base 8 — Upper bound on s

There is no (59, 141, 2916)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 21 759932 748547 172268 296381 995177 079571 968511 413391 755089 677995 998835 030096 074351 339817 047410 021711 885079 545198 355922 111605 247560 > 8¹⁴¹ [i]