MinT - Best Known (128−87, 128, s)-Nets in Base 8

Best Known (128−87, 128, s)-Nets in Base 8

(128−87, 128, 98)-Net over F₈ — Constructive and digital

Digital (41, 128, 98)-net over F₈, using

t-expansion [i] based on digital (37, 128, 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]

(128−87, 128, 129)-Net over F₈ — Digital

Digital (41, 128, 129)-net over F₈, using

t-expansion [i] based on digital (38, 128, 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]

(128−87, 128, 1094)-Net in Base 8 — Upper bound on s

There is no (41, 128, 1095)-net in base 8, because

1 times m-reduction [i] would yield (41, 127, 1095)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 5 091476 305883 667266 464900 310658 214971 860112 503824 658285 970715 782920 696213 826259 868642 200353 881058 833332 676965 101600 > 8¹²⁷ [i]