MinT - Best Known (143−107, 143, s)-Nets in Base 8

Best Known (143−107, 143, s)-Nets in Base 8

(143−107, 143, 65)-Net over F₈ — Constructive and digital

Digital (36, 143, 65)-net over F₈, using

t-expansion [i] based on digital (14, 143, 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]

(143−107, 143, 112)-Net over F₈ — Digital

Digital (36, 143, 112)-net over F₈, using

t-expansion [i] based on digital (35, 143, 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]

(143−107, 143, 740)-Net in Base 8 — Upper bound on s

There is no (36, 143, 741)-net in base 8, because

1 times m-reduction [i] would yield (36, 142, 741)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 184 770906 193618 861570 666471 266162 173649 627475 201092 984240 329317 452796 752253 214197 222019 211633 871905 046397 394066 450753 173740 297312 > 8¹⁴² [i]