MinT - Best Known (41, 41+121, s)-Nets in Base 8

Best Known (41, 41+121, s)-Nets in Base 8

(41, 41+121, 98)-Net over F₈ — Constructive and digital

Digital (41, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 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+121, 129)-Net over F₈ — Digital

Digital (41, 162, 129)-net over F₈, using

t-expansion [i] based on digital (38, 162, 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+121, 840)-Net in Base 8 — Upper bound on s

There is no (41, 162, 841)-net in base 8, because

1 times m-reduction [i] would yield (41, 161, 841)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 858876 926196 728006 585341 804086 976621 316573 572830 458973 629007 175567 177004 988205 641428 174832 557042 153317 808249 392303 932243 922720 998953 083658 548944 > 8¹⁶¹ [i]