MinT - Best Known (142−117, 142, s)-Nets in Base 8

Best Known (142−117, 142, s)-Nets in Base 8

(142−117, 142, 65)-Net over F₈ — Constructive and digital

Digital (25, 142, 65)-net over F₈, using

t-expansion [i] based on digital (14, 142, 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]

(142−117, 142, 86)-Net over F₈ — Digital

Digital (25, 142, 86)-net over F₈, using

net from sequence [i] based on digital (25, 85)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 25 and N(F) ≥ 86, using
  - a curve from the manYPoints database [i]

(142−117, 142, 467)-Net in Base 8 — Upper bound on s

There is no (25, 142, 468)-net in base 8, because

1 times m-reduction [i] would yield (25, 141, 468)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 24 282490 368844 440723 911426 407889 287446 584950 271835 029334 552271 829386 242824 944872 411066 947502 911674 421232 210232 816276 738222 990408 > 8¹⁴¹ [i]