MinT - Best Known (53, 53+108, s)-Nets in Base 8

Best Known (53, 53+108, s)-Nets in Base 8

(53, 53+108, 98)-Net over F₈ — Constructive and digital

Digital (53, 161, 98)-net over F₈, using

t-expansion [i] based on digital (37, 161, 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]

(53, 53+108, 144)-Net over F₈ — Digital

Digital (53, 161, 144)-net over F₈, using

t-expansion [i] based on digital (45, 161, 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]

(53, 53+108, 1441)-Net in Base 8 — Upper bound on s

There is no (53, 161, 1442)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 249852 686881 654332 242600 985633 161049 438500 251053 395764 958269 723334 707910 200268 501046 908886 747636 305900 715395 073681 644834 254572 264619 502890 352064 > 8¹⁶¹ [i]