MinT - Best Known (78−51, 78, s)-Nets in Base 8

Best Known (78−51, 78, s)-Nets in Base 8

(78−51, 78, 65)-Net over F₈ — Constructive and digital

Digital (27, 78, 65)-net over F₈, using

t-expansion [i] based on digital (14, 78, 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]

(78−51, 78, 96)-Net over F₈ — Digital

Digital (27, 78, 96)-net over F₈, using

net from sequence [i] based on digital (27, 95)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 27 and N(F) ≥ 96, using
  - a curve from the manYPoints database [i]

(78−51, 78, 863)-Net in Base 8 — Upper bound on s

There is no (27, 78, 864)-net in base 8, because

1 times m-reduction [i] would yield (27, 77, 864)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3487 693661 837023 053579 492780 231824 223459 740963 876403 760032 077144 716291 > 8⁷⁷ [i]