MinT - Best Known (28, 28+111, s)-Nets in Base 8

Best Known (28, 28+111, s)-Nets in Base 8

(28, 28+111, 65)-Net over F₈ — Constructive and digital

Digital (28, 139, 65)-net over F₈, using

t-expansion [i] based on digital (14, 139, 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]

(28, 28+111, 97)-Net over F₈ — Digital

Digital (28, 139, 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]

(28, 28+111, 528)-Net in Base 8 — Upper bound on s

There is no (28, 139, 529)-net in base 8, because

1 times m-reduction [i] would yield (28, 138, 529)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 46129 650306 083284 211351 654088 213086 742662 401505 358466 277415 740792 754797 271056 599259 452220 415641 495292 317639 012819 508346 490368 > 8¹³⁸ [i]