MinT - Best Known (34, 151, s)-Nets in Base 8

Best Known (34, 151, s)-Nets in Base 8

(34, 151, 65)-Net over F₈ — Constructive and digital

Digital (34, 151, 65)-net over F₈, using

t-expansion [i] based on digital (14, 151, 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]

(34, 151, 98)-Net over F₈ — Digital

Digital (34, 151, 98)-net over F₈, using

net from sequence [i] based on digital (34, 97)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 34 and N(F) ≥ 98, using
  - a curve from the manYPoints database [i]

(34, 151, 658)-Net in Base 8 — Upper bound on s

There is no (34, 151, 659)-net in base 8, because

1 times m-reduction [i] would yield (34, 150, 659)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3070 422878 057409 817522 864344 877867 360953 258184 696598 756298 824984 947703 109239 644363 632341 959574 244149 755584 996680 013037 951924 110783 051120 > 8¹⁵⁰ [i]