MinT - Best Known (173−138, 173, s)-Nets in Base 8

Best Known (173−138, 173, s)-Nets in Base 8

(173−138, 173, 65)-Net over F₈ — Constructive and digital

Digital (35, 173, 65)-net over F₈, using

t-expansion [i] based on digital (14, 173, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(173−138, 173, 112)-Net over F₈ — Digital

Digital (35, 173, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(173−138, 173, 653)-Net in Base 8 — Upper bound on s

There is no (35, 173, 654)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 834147 760010 219322 968207 424553 316925 019672 119090 080027 729492 396424 854410 619553 610657 084835 977846 525427 092214 972895 315724 841900 733137 208991 934650 917393 575646 > 8¹⁷³ [i]