MinT - Best Known (164−129, 164, s)-Nets in Base 8

Best Known (164−129, 164, s)-Nets in Base 8

(164−129, 164, 65)-Net over F₈ — Constructive and digital

Digital (35, 164, 65)-net over F₈, using

t-expansion [i] based on digital (14, 164, 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]

(164−129, 164, 112)-Net over F₈ — Digital

Digital (35, 164, 112)-net over F₈, using

net from sequence [i] based on digital (35, 111)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 35 and N(F) ≥ 112, using
  - a curve from the manYPoints database [i]

(164−129, 164, 663)-Net in Base 8 — Upper bound on s

There is no (35, 164, 664)-net in base 8, because

1 times m-reduction [i] would yield (35, 163, 664)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 1680 820663 866472 043371 313394 772406 838525 740853 327743 167529 146993 471026 582179 638912 802867 153815 166959 997443 220981 248846 525792 706384 630080 973245 573926 > 8¹⁶³ [i]