MinT - Best Known (114−78, 114, s)-Nets in Base 8

Best Known (114−78, 114, s)-Nets in Base 8

(114−78, 114, 65)-Net over F₈ — Constructive and digital

Digital (36, 114, 65)-net over F₈, using

t-expansion [i] based on digital (14, 114, 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]

(114−78, 114, 112)-Net over F₈ — Digital

Digital (36, 114, 112)-net over F₈, using

t-expansion [i] based on digital (35, 114, 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]

(114−78, 114, 935)-Net in Base 8 — Upper bound on s

There is no (36, 114, 936)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9 216094 747406 741886 557763 199542 692285 319621 683248 860889 769027 066165 458304 430523 907299 937049 130154 331819 > 8¹¹⁴ [i]