MinT - Best Known (167−125, 167, s)-Nets in Base 8

Best Known (167−125, 167, s)-Nets in Base 8

(167−125, 167, 98)-Net over F₈ — Constructive and digital

Digital (42, 167, 98)-net over F₈, using

t-expansion [i] based on digital (37, 167, 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]

(167−125, 167, 129)-Net over F₈ — Digital

Digital (42, 167, 129)-net over F₈, using

t-expansion [i] based on digital (38, 167, 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]

(167−125, 167, 856)-Net in Base 8 — Upper bound on s

There is no (42, 167, 857)-net in base 8, because

1 times m-reduction [i] would yield (42, 166, 857)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 864109 565894 819374 571781 243035 229843 119558 468722 722767 418121 300543 425526 731192 160914 405409 781093 543146 163259 710439 154491 231245 774823 084887 171326 386016 > 8¹⁶⁶ [i]