MinT - Best Known (128−89, 128, s)-Nets in Base 8

Best Known (128−89, 128, s)-Nets in Base 8

(128−89, 128, 98)-Net over F₈ — Constructive and digital

Digital (39, 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]

(128−89, 128, 129)-Net over F₈ — Digital

Digital (39, 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]

(128−89, 128, 968)-Net in Base 8 — Upper bound on s

There is no (39, 128, 969)-net in base 8, because

1 times m-reduction [i] would yield (39, 127, 969)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 4 939961 752456 308848 629915 710770 600894 040404 811526 188981 162538 119739 794241 205380 528109 829632 553843 243738 011573 867600 > 8¹²⁷ [i]