MinT - Best Known (173−143, 173, s)-Nets in Base 8

Best Known (173−143, 173, s)-Nets in Base 8

(173−143, 173, 65)-Net over F₈ — Constructive and digital

Digital (30, 173, 65)-net over F₈, using

t-expansion [i] based on digital (14, 173, 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]

(173−143, 173, 97)-Net over F₈ — Digital

Digital (30, 173, 97)-net over F₈, using

t-expansion [i] based on digital (28, 173, 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]

(173−143, 173, 555)-Net in Base 8 — Upper bound on s

There is no (30, 173, 556)-net in base 8, because

3 times m-reduction [i] would yield (30, 170, 556)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3352 088021 544426 433648 519240 841917 343084 912695 811178 526751 468297 465284 130931 241691 086824 276805 630757 505106 872435 799877 074587 898261 513639 441427 471516 174064 > 8¹⁷⁰ [i]