MinT - Best Known (170−142, 170, s)-Nets in Base 8

Best Known (170−142, 170, s)-Nets in Base 8

(170−142, 170, 65)-Net over F₈ — Constructive and digital

Digital (28, 170, 65)-net over F₈, using

t-expansion [i] based on digital (14, 170, 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]

(170−142, 170, 97)-Net over F₈ — Digital

Digital (28, 170, 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]

(170−142, 170, 520)-Net in Base 8 — Upper bound on s

There is no (28, 170, 521)-net in base 8, because

6 times m-reduction [i] would yield (28, 164, 521)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13168 109730 625848 946818 378710 971050 463162 709584 123653 918507 065023 804393 133542 456638 101641 569295 225882 667917 765440 802118 219970 306065 204362 154156 393168 > 8¹⁶⁴ [i]