MinT - Best Known (173−124, 173, s)-Nets in Base 8

Best Known (173−124, 173, s)-Nets in Base 8

(173−124, 173, 98)-Net over F₈ — Constructive and digital

Digital (49, 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]

(173−124, 173, 144)-Net over F₈ — Digital

Digital (49, 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]

(173−124, 173, 1092)-Net in Base 8 — Upper bound on s

There is no (49, 173, 1093)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 719674 031010 736139 521598 437713 759884 284004 021222 197295 033904 442186 835632 249778 400917 234627 389472 173378 367071 902708 624313 680203 259371 459358 058916 443981 759008 > 8¹⁷³ [i]