MinT - Best Known (130−95, 130, s)-Nets in Base 8

Best Known (130−95, 130, s)-Nets in Base 8

(130−95, 130, 65)-Net over F₈ — Constructive and digital

Digital (35, 130, 65)-net over F₈, using

t-expansion [i] based on digital (14, 130, 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]

(130−95, 130, 112)-Net over F₈ — Digital

Digital (35, 130, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(130−95, 130, 760)-Net in Base 8 — Upper bound on s

There is no (35, 130, 761)-net in base 8, because

1 times m-reduction [i] would yield (35, 129, 761)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 320 056021 490167 240794 119770 248271 868310 273556 364643 550785 684218 580412 966365 857852 676176 753000 073605 785566 948234 867408 > 8¹²⁹ [i]