MinT - Best Known (60, 60+108, s)-Nets in Base 8

Best Known (60, 60+108, s)-Nets in Base 8

(60, 60+108, 98)-Net over F₈ — Constructive and digital

Digital (60, 168, 98)-net over F₈, using

t-expansion [i] based on digital (37, 168, 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]

(60, 60+108, 144)-Net over F₈ — Digital

Digital (60, 168, 144)-net over F₈, using

t-expansion [i] based on digital (45, 168, 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]

(60, 60+108, 1898)-Net in Base 8 — Upper bound on s

There is no (60, 168, 1899)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 53 565358 524126 650635 488776 446835 172199 220490 265226 627364 667278 274349 012168 852130 709097 601863 953093 649350 144097 963102 165800 933760 349826 757689 681710 076472 > 8¹⁶⁸ [i]