MinT - Best Known (62, 62+102, s)-Nets in Base 8

Best Known (62, 62+102, s)-Nets in Base 8

(62, 62+102, 98)-Net over F₈ — Constructive and digital

Digital (62, 164, 98)-net over F₈, using

t-expansion [i] based on digital (37, 164, 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]

(62, 62+102, 144)-Net over F₈ — Digital

Digital (62, 164, 144)-net over F₈, using

t-expansion [i] based on digital (45, 164, 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]

(62, 62+102, 2241)-Net in Base 8 — Upper bound on s

There is no (62, 164, 2242)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12796 874061 265862 785588 845931 230848 829702 315268 369264 345870 777864 524588 611967 964797 844945 853971 417517 248043 689175 283806 667004 456566 313140 459866 535520 > 8¹⁶⁴ [i]