MinT - Best Known (43, 106, s)-Nets in Base 8

Best Known (43, 106, s)-Nets in Base 8

(43, 106, 98)-Net over F₈ — Constructive and digital

Digital (43, 106, 98)-net over F₈, using

t-expansion [i] based on digital (37, 106, 98)-net over F₈, using
- net from sequence [i] based on digital (37, 97)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 98, using
    - F₅ from the tower of function fields over F₈ by van der Geer and van der Vlugt [i]

(43, 106, 129)-Net over F₈ — Digital

Digital (43, 106, 129)-net over F₈, using

t-expansion [i] based on digital (38, 106, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(43, 106, 2011)-Net in Base 8 — Upper bound on s

There is no (43, 106, 2012)-net in base 8, because

1 times m-reduction [i] would yield (43, 105, 2012)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 66755 803761 648221 308023 881111 334782 728089 407664 672405 012599 544925 733701 538276 576554 392265 579440 > 8¹⁰⁵ [i]