MinT - Best Known (153−119, 153, s)-Nets in Base 8

Best Known (153−119, 153, s)-Nets in Base 8

(153−119, 153, 65)-Net over F₈ — Constructive and digital

Digital (34, 153, 65)-net over F₈, using

t-expansion [i] based on digital (14, 153, 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]

(153−119, 153, 98)-Net over F₈ — Digital

Digital (34, 153, 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]

(153−119, 153, 654)-Net in Base 8 — Upper bound on s

There is no (34, 153, 655)-net in base 8, because

1 times m-reduction [i] would yield (34, 152, 655)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 189967 947844 569538 657225 391396 827104 909610 757353 224491 047889 448795 605464 108026 419485 365266 967895 637976 155011 114522 164410 193088 453548 096928 > 8¹⁵² [i]