MinT - Best Known (156−112, 156, s)-Nets in Base 8

Best Known (156−112, 156, s)-Nets in Base 8

(156−112, 156, 98)-Net over F₈ — Constructive and digital

Digital (44, 156, 98)-net over F₈, using

t-expansion [i] based on digital (37, 156, 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]

(156−112, 156, 130)-Net over F₈ — Digital

Digital (44, 156, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(156−112, 156, 981)-Net in Base 8 — Upper bound on s

There is no (44, 156, 982)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 770 370282 791284 144420 448241 668233 205368 267591 888515 729934 295942 817218 510961 052079 129517 454610 504714 216408 003039 693813 102411 716485 055723 906120 > 8¹⁵⁶ [i]