MinT - Best Known (173−130, 173, s)-Nets in Base 8

Best Known (173−130, 173, s)-Nets in Base 8

(173−130, 173, 98)-Net over F₈ — Constructive and digital

Digital (43, 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]

(173−130, 173, 129)-Net over F₈ — Digital

Digital (43, 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]

(173−130, 173, 865)-Net in Base 8 — Upper bound on s

There is no (43, 173, 866)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 782554 604957 681520 564012 952908 263837 136758 771678 351958 010177 686382 828125 207799 389149 405223 042075 725614 352422 355276 794527 509397 062139 047973 068342 373091 703445 > 8¹⁷³ [i]