MinT - Best Known (76−47, 76, s)-Nets in Base 8

Best Known (76−47, 76, s)-Nets in Base 8

(76−47, 76, 65)-Net over F₈ — Constructive and digital

Digital (29, 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]

(76−47, 76, 97)-Net over F₈ — Digital

Digital (29, 76, 97)-net over F₈, using

t-expansion [i] based on digital (28, 76, 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]

(76−47, 76, 1172)-Net in Base 8 — Upper bound on s

There is no (29, 76, 1173)-net in base 8, because

1 times m-reduction [i] would yield (29, 75, 1173)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 54 838383 321862 839130 304241 870333 638947 374189 199708 984837 049654 083456 > 8⁷⁵ [i]