MinT - Best Known (120−81, 120, s)-Nets in Base 8

Best Known (120−81, 120, s)-Nets in Base 8

(120−81, 120, 98)-Net over F₈ — Constructive and digital

Digital (39, 120, 98)-net over F₈, using

t-expansion [i] based on digital (37, 120, 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]

(120−81, 120, 129)-Net over F₈ — Digital

Digital (39, 120, 129)-net over F₈, using

t-expansion [i] based on digital (38, 120, 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]

(120−81, 120, 1069)-Net in Base 8 — Upper bound on s

There is no (39, 120, 1070)-net in base 8, because

1 times m-reduction [i] would yield (39, 119, 1070)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 294752 520143 054472 476790 235641 029420 309855 564403 008920 395767 345645 260746 185227 137528 969366 486073 938065 330655 > 8¹¹⁹ [i]