MinT - Best Known (154−119, 154, s)-Nets in Base 8

Best Known (154−119, 154, s)-Nets in Base 8

(154−119, 154, 65)-Net over F₈ — Constructive and digital

Digital (35, 154, 65)-net over F₈, using

t-expansion [i] based on digital (14, 154, 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]

(154−119, 154, 112)-Net over F₈ — Digital

Digital (35, 154, 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]

(154−119, 154, 679)-Net in Base 8 — Upper bound on s

There is no (35, 154, 680)-net in base 8, because

1 times m-reduction [i] would yield (35, 153, 680)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1 545271 071171 207486 021211 210571 840702 953267 572029 962524 972514 200740 627943 137462 941669 197870 515747 401612 223418 786863 893788 838915 202065 385616 > 8¹⁵³ [i]