MinT - Best Known (70−53, 70, s)-Nets in Base 8

Best Known (70−53, 70, s)-Nets in Base 8

(70−53, 70, 65)-Net over F₈ — Constructive and digital

Digital (17, 70, 65)-net over F₈, using

t-expansion [i] based on digital (14, 70, 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]

(70−53, 70, 359)-Net in Base 8 — Upper bound on s

There is no (17, 70, 360)-net in base 8, because

1 times m-reduction [i] would yield (17, 69, 360)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 209 834380 120760 618642 841041 443233 194195 548087 576048 766616 897436 > 8⁶⁹ [i]