MinT - Best Known (52−45, 52, s)-Nets in Base 8

Best Known (52−45, 52, s)-Nets in Base 8

(52−45, 52, 34)-Net over F₈ — Constructive and digital

Digital (7, 52, 34)-net over F₈, using

net from sequence [i] based on digital (7, 33)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 7 and N(F) ≥ 34, using
  - a function field by SÃ©mirat [i]

(52−45, 52, 96)-Net in Base 8 — Upper bound on s

There is no (7, 52, 97)-net in base 8, because

extracting embedded orthogonal array [i] would yield OA(8⁵², 97, S₈, 45), but
- the linear programming bound shows that MÂ â‰¥ 490 054689 866201 591716 719854 885577 526473 405299 503418 620051 386154 961085 815041 551054 696814 746334 658560 / 5107 878884 902542 641022 981807 927034 033745 065727 789561 > 8⁵² [i]