MinT - Best Known (165−148, 165, s)-Nets in Base 8

Best Known (165−148, 165, s)-Nets in Base 8

(165−148, 165, 65)-Net over F₈ — Constructive and digital

Digital (17, 165, 65)-net over F₈, using

t-expansion [i] based on digital (14, 165, 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]

(165−148, 165, 136)-Net in Base 8 — Upper bound on s

There is no (17, 165, 137)-net in base 8, because

44 times m-reduction [i] would yield (17, 121, 137)-net in base 8, but
- extracting embedded orthogonal array [i] would yield OA(8¹²¹, 137, S₈, 104), but
  - the linear programming bound shows that MÂ â‰¥ 13066 856935 963523 721024 625401 270709 435452 350217 785478 549632 311553 515794 037630 134130 713931 717708 202057 690742 978515 268863 524864 / 568 730779 782165 > 8¹²¹ [i]