MinT - Best Known (132−96, 132, s)-Nets in Base 8

Best Known (132−96, 132, s)-Nets in Base 8

(132−96, 132, 65)-Net over F₈ — Constructive and digital

Digital (36, 132, 65)-net over F₈, using

t-expansion [i] based on digital (14, 132, 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]

(132−96, 132, 112)-Net over F₈ — Digital

Digital (36, 132, 112)-net over F₈, using

t-expansion [i] based on digital (35, 132, 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]

(132−96, 132, 785)-Net in Base 8 — Upper bound on s

There is no (36, 132, 786)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 170770 854593 875201 198988 128463 208039 438759 026670 390308 189433 600519 844261 019692 029745 394633 085872 164718 035341 062835 455000 > 8¹³² [i]