MinT - Best Known (122−81, 122, s)-Nets in Base 8

Best Known (122−81, 122, s)-Nets in Base 8

(122−81, 122, 98)-Net over F₈ — Constructive and digital

Digital (41, 122, 98)-net over F₈, using

t-expansion [i] based on digital (37, 122, 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]

(122−81, 122, 129)-Net over F₈ — Digital

Digital (41, 122, 129)-net over F₈, using

t-expansion [i] based on digital (38, 122, 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]

(122−81, 122, 1189)-Net in Base 8 — Upper bound on s

There is no (41, 122, 1190)-net in base 8, because

1 times m-reduction [i] would yield (41, 121, 1190)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 18 885507 456950 698161 424827 391582 287984 836840 719346 295144 668790 883185 769493 709154 321332 785413 102569 237020 436432 > 8¹²¹ [i]