MinT - Best Known (118−75, 118, s)-Nets in Base 8

Best Known (118−75, 118, s)-Nets in Base 8

(118−75, 118, 98)-Net over F₈ — Constructive and digital

Digital (43, 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]

(118−75, 118, 129)-Net over F₈ — Digital

Digital (43, 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]

(118−75, 118, 1478)-Net in Base 8 — Upper bound on s

There is no (43, 118, 1479)-net in base 8, because

1 times m-reduction [i] would yield (43, 117, 1479)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4661 889289 700275 812228 977132 488316 303999 808298 409138 601538 650972 150981 501802 203456 231268 704520 204043 557268 > 8¹¹⁷ [i]