MinT - Best Known (100−78, 100, s)-Nets in Base 8

Best Known (100−78, 100, s)-Nets in Base 8

(100−78, 100, 65)-Net over F₈ — Constructive and digital

Digital (22, 100, 65)-net over F₈, using

t-expansion [i] based on digital (14, 100, 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]

(100−78, 100, 76)-Net over F₈ — Digital

Digital (22, 100, 76)-net over F₈, using

t-expansion [i] based on digital (20, 100, 76)-net over F₈, using
- net from sequence [i] based on digital (20, 75)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 20 and N(F) ≥ 76, using
    - a curve from the manYPoints database [i]

(100−78, 100, 430)-Net in Base 8 — Upper bound on s

There is no (22, 100, 431)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 2 080696 241095 254983 069898 756884 462054 583480 352062 269687 354812 557468 537121 030747 474006 261952 > 8¹⁰⁰ [i]