MinT - Best Known (76−57, 76, s)-Nets in Base 8

Best Known (76−57, 76, s)-Nets in Base 8

(76−57, 76, 65)-Net over F₈ — Constructive and digital

Digital (19, 76, 65)-net over F₈, using

t-expansion [i] based on digital (14, 76, 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]

(76−57, 76, 406)-Net in Base 8 — Upper bound on s

There is no (19, 76, 407)-net in base 8, because

1 times m-reduction [i] would yield (19, 75, 407)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 56 612753 843896 869274 975838 709757 734475 346507 539064 688497 395479 356400 > 8⁷⁵ [i]