MinT - Best Known (106−80, 106, s)-Nets in Base 8

Best Known (106−80, 106, s)-Nets in Base 8

(106−80, 106, 65)-Net over F₈ — Constructive and digital

Digital (26, 106, 65)-net over F₈, using

t-expansion [i] based on digital (14, 106, 65)-net over F₈, using
- net from sequence [i] based on digital (14, 64)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 14 and N(F) ≥ 65, using
    - the Suzuki function field over F₈ [i]

(106−80, 106, 86)-Net over F₈ — Digital

Digital (26, 106, 86)-net over F₈, using

t-expansion [i] based on digital (25, 106, 86)-net over F₈, using
- net from sequence [i] based on digital (25, 85)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
    - a curve from the manYPoints database [i]

(106−80, 106, 532)-Net in Base 8 — Upper bound on s

There is no (26, 106, 533)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 567139 688197 863184 210662 209115 863247 835341 768690 325658 771019 141639 714489 196838 662905 779596 654560 > 8¹⁰⁶ [i]