MinT - Best Known (172−106, 172, s)-Nets in Base 8

Best Known (172−106, 172, s)-Nets in Base 8

(172−106, 172, 98)-Net over F₈ — Constructive and digital

Digital (66, 172, 98)-net over F₈, using

t-expansion [i] based on digital (37, 172, 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]

(172−106, 172, 144)-Net over F₈ — Digital

Digital (66, 172, 144)-net over F₈, using

t-expansion [i] based on digital (45, 172, 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]

(172−106, 172, 2475)-Net in Base 8 — Upper bound on s

There is no (66, 172, 2476)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 217172 946356 957482 435326 501114 028583 623115 443468 927987 875155 746613 454313 115909 671075 914451 349159 720048 882242 666698 680789 157338 020910 999396 579985 157180 850352 > 8¹⁷² [i]