MinT - Best Known (118−77, 118, s)-Nets in Base 8

Best Known (118−77, 118, s)-Nets in Base 8

(118−77, 118, 98)-Net over F₈ — Constructive and digital

Digital (41, 118, 98)-net over F₈, using

t-expansion [i] based on digital (37, 118, 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]

(118−77, 118, 129)-Net over F₈ — Digital

Digital (41, 118, 129)-net over F₈, using

t-expansion [i] based on digital (38, 118, 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]

(118−77, 118, 1271)-Net in Base 8 — Upper bound on s

There is no (41, 118, 1272)-net in base 8, because

1 times m-reduction [i] would yield (41, 117, 1272)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4694 396596 186375 015147 888412 670148 266366 767446 140722 521800 282592 444863 571554 909326 917455 375112 057891 168583 > 8¹¹⁷ [i]