MinT - Best Known (171−139, 171, s)-Nets in Base 8

Best Known (171−139, 171, s)-Nets in Base 8

(171−139, 171, 65)-Net over F₈ — Constructive and digital

Digital (32, 171, 65)-net over F₈, using

t-expansion [i] based on digital (14, 171, 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]

(171−139, 171, 97)-Net over F₈ — Digital

Digital (32, 171, 97)-net over F₈, using

t-expansion [i] based on digital (28, 171, 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]

(171−139, 171, 593)-Net in Base 8 — Upper bound on s

There is no (32, 171, 594)-net in base 8, because

1 times m-reduction [i] would yield (32, 170, 594)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3653 141757 338348 271900 202678 757879 794740 074983 562767 515081 042552 107507 558405 643541 914662 082823 021929 430021 475088 508875 982657 430553 331755 207865 322506 902820 > 8¹⁷⁰ [i]