MinT - Best Known (124−101, 124, s)-Nets in Base 8

Best Known (124−101, 124, s)-Nets in Base 8

(124−101, 124, 65)-Net over F₈ — Constructive and digital

Digital (23, 124, 65)-net over F₈, using

t-expansion [i] based on digital (14, 124, 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]

(124−101, 124, 76)-Net over F₈ — Digital

Digital (23, 124, 76)-net over F₈, using

t-expansion [i] based on digital (20, 124, 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]

(124−101, 124, 432)-Net in Base 8 — Upper bound on s

There is no (23, 124, 433)-net in base 8, because

1 times m-reduction [i] would yield (23, 123, 433)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1253 085093 261949 167477 302001 345224 189147 422871 360161 231428 698656 367032 802312 225075 873868 955828 912823 757191 052672 > 8¹²³ [i]