MinT - Best Known (65, 65+108, s)-Nets in Base 8

Best Known (65, 65+108, s)-Nets in Base 8

(65, 65+108, 98)-Net over F₈ — Constructive and digital

Digital (65, 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]

(65, 65+108, 144)-Net over F₈ — Digital

Digital (65, 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]

(65, 65+108, 2308)-Net in Base 8 — Upper bound on s

There is no (65, 173, 2309)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 739069 865172 779776 129359 606157 097650 303411 932188 330988 080500 427115 330111 917623 086134 376813 865357 372866 919086 023583 279667 606398 677309 812136 545218 087298 293376 > 8¹⁷³ [i]