MinT - Best Known (125−89, 125, s)-Nets in Base 8

Best Known (125−89, 125, s)-Nets in Base 8

(125−89, 125, 65)-Net over F₈ — Constructive and digital

Digital (36, 125, 65)-net over F₈, using

t-expansion [i] based on digital (14, 125, 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]

(125−89, 125, 112)-Net over F₈ — Digital

Digital (36, 125, 112)-net over F₈, using

t-expansion [i] based on digital (35, 125, 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]

(125−89, 125, 837)-Net in Base 8 — Upper bound on s

There is no (36, 125, 838)-net in base 8, because

1 times m-reduction [i] would yield (36, 124, 838)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9996 705115 427239 678253 824602 082381 795700 127041 693983 120173 840345 074436 055716 920044 246815 875764 517990 083256 975736 > 8¹²⁴ [i]