MinT - Best Known (59, 59+114, s)-Nets in Base 8

Best Known (59, 59+114, s)-Nets in Base 8

(59, 59+114, 98)-Net over F₈ — Constructive and digital

Digital (59, 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]

(59, 59+114, 144)-Net over F₈ — Digital

Digital (59, 173, 144)-net over F₈, using

t-expansion [i] based on digital (45, 173, 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, 59+114, 1701)-Net in Base 8 — Upper bound on s

There is no (59, 173, 1702)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 755901 620047 235731 979270 750792 045515 174649 972626 229888 097651 738128 521554 243107 721717 556752 235751 303443 655607 907460 371660 640383 443672 891193 825112 890580 628016 > 8¹⁷³ [i]