MinT - Best Known (155−120, 155, s)-Nets in Base 8

Best Known (155−120, 155, s)-Nets in Base 8

(155−120, 155, 65)-Net over F₈ — Constructive and digital

Digital (35, 155, 65)-net over F₈, using

t-expansion [i] based on digital (14, 155, 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]

(155−120, 155, 112)-Net over F₈ — Digital

Digital (35, 155, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(155−120, 155, 675)-Net in Base 8 — Upper bound on s

There is no (35, 155, 676)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 97 328231 054981 959733 507867 153133 040962 546676 898944 896378 703460 230131 855944 918571 162383 814940 838072 691793 403248 340638 998471 595166 858038 661408 > 8¹⁵⁵ [i]