MinT - Best Known (41, 41+132, s)-Nets in Base 8

Best Known (41, 41+132, s)-Nets in Base 8

(41, 41+132, 98)-Net over F₈ — Constructive and digital

Digital (41, 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]

(41, 41+132, 129)-Net over F₈ — Digital

Digital (41, 173, 129)-net over F₈, using

t-expansion [i] based on digital (38, 173, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(41, 41+132, 804)-Net in Base 8 — Upper bound on s

There is no (41, 173, 805)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 809881 047664 645064 174546 153977 281236 563397 466962 100199 997170 494077 185470 229863 868351 633161 120620 949799 853612 092023 807258 503262 417146 287266 178366 178409 139304 > 8¹⁷³ [i]