MinT - Best Known (54, 54+86, s)-Nets in Base 8

Best Known (54, 54+86, s)-Nets in Base 8

(54, 54+86, 98)-Net over F₈ — Constructive and digital

Digital (54, 140, 98)-net over F₈, using

t-expansion [i] based on digital (37, 140, 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]

(54, 54+86, 144)-Net over F₈ — Digital

Digital (54, 140, 144)-net over F₈, using

t-expansion [i] based on digital (45, 140, 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]

(54, 54+86, 2075)-Net in Base 8 — Upper bound on s

There is no (54, 140, 2076)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 757298 879772 825607 423557 782363 303862 914365 586579 774265 469493 960152 730306 650946 252272 261560 754407 676230 611109 195177 061456 776256 > 8¹⁴⁰ [i]