MinT - Best Known (151−121, 151, s)-Nets in Base 8

Best Known (151−121, 151, s)-Nets in Base 8

(151−121, 151, 65)-Net over F₈ — Constructive and digital

Digital (30, 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]

(151−121, 151, 97)-Net over F₈ — Digital

Digital (30, 151, 97)-net over F₈, using

t-expansion [i] based on digital (28, 151, 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]

(151−121, 151, 562)-Net in Base 8 — Upper bound on s

There is no (30, 151, 563)-net in base 8, because

1 times m-reduction [i] would yield (30, 150, 563)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3092 972387 238427 161371 117220 393050 083392 621351 165497 377508 818163 696686 582240 254448 206971 290577 971584 718711 185535 361119 131657 240801 655424 > 8¹⁵⁰ [i]