MinT - Best Known (170−139, 170, s)-Nets in Base 8

Best Known (170−139, 170, s)-Nets in Base 8

(170−139, 170, 65)-Net over F₈ — Constructive and digital

Digital (31, 170, 65)-net over F₈, using

t-expansion [i] based on digital (14, 170, 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]

(170−139, 170, 97)-Net over F₈ — Digital

Digital (31, 170, 97)-net over F₈, using

t-expansion [i] based on digital (28, 170, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(170−139, 170, 574)-Net in Base 8 — Upper bound on s

There is no (31, 170, 575)-net in base 8, because

1 times m-reduction [i] would yield (31, 169, 575)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 450 733041 317087 064778 470506 436422 723946 345296 796095 619492 986772 984219 639027 846456 690127 349057 405771 333717 645056 648635 591636 749382 047673 518957 861364 150512 > 8¹⁶⁹ [i]