MinT - Best Known (112−80, 112, s)-Nets in Base 8

Best Known (112−80, 112, s)-Nets in Base 8

(112−80, 112, 65)-Net over F₈ — Constructive and digital

Digital (32, 112, 65)-net over F₈, using

t-expansion [i] based on digital (14, 112, 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]

(112−80, 112, 97)-Net over F₈ — Digital

Digital (32, 112, 97)-net over F₈, using

t-expansion [i] based on digital (28, 112, 97)-net over F₈, using
- net from sequence [i] based on digital (28, 96)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 28 and N(F) ≥ 97, using
    - a curve from the manYPoints database [i]

(112−80, 112, 735)-Net in Base 8 — Upper bound on s

There is no (32, 112, 736)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 140221 626621 001548 592828 727233 845967 456048 835531 827434 091738 126015 427491 596126 275576 688755 690770 733606 > 8¹¹² [i]