MinT - Best Known (157−116, 157, s)-Nets in Base 8

Best Known (157−116, 157, s)-Nets in Base 8

(157−116, 157, 98)-Net over F₈ — Constructive and digital

Digital (41, 157, 98)-net over F₈, using

t-expansion [i] based on digital (37, 157, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(157−116, 157, 129)-Net over F₈ — Digital

Digital (41, 157, 129)-net over F₈, using

t-expansion [i] based on digital (38, 157, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(157−116, 157, 856)-Net in Base 8 — Upper bound on s

There is no (41, 157, 857)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 6358 215897 453482 569840 715823 208383 395990 354050 752895 354055 515360 636762 065468 260645 257164 547147 879676 770206 831385 392468 520793 058452 686462 422240 > 8¹⁵⁷ [i]