MinT - Best Known (106−75, 106, s)-Nets in Base 8

Best Known (106−75, 106, s)-Nets in Base 8

(106−75, 106, 65)-Net over F₈ — Constructive and digital

Digital (31, 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]

(106−75, 106, 97)-Net over F₈ — Digital

Digital (31, 106, 97)-net over F₈, using

t-expansion [i] based on digital (28, 106, 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]

(106−75, 106, 741)-Net in Base 8 — Upper bound on s

There is no (31, 106, 742)-net in base 8, because

1 times m-reduction [i] would yield (31, 105, 742)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 67123 072645 260650 412132 456973 945014 080763 918803 142755 700400 646513 767264 021550 067683 045332 737717 > 8¹⁰⁵ [i]