MinT - Best Known (125−81, 125, s)-Nets in Base 8

Best Known (125−81, 125, s)-Nets in Base 8

(125−81, 125, 98)-Net over F₈ — Constructive and digital

Digital (44, 125, 98)-net over F₈, using

t-expansion [i] based on digital (37, 125, 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]

(125−81, 125, 130)-Net over F₈ — Digital

Digital (44, 125, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(125−81, 125, 1394)-Net in Base 8 — Upper bound on s

There is no (44, 125, 1395)-net in base 8, because

1 times m-reduction [i] would yield (44, 124, 1395)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9655 463789 447633 222101 933017 312237 386754 425469 003294 058850 169607 982099 591379 464846 263623 127949 960683 450590 431550 > 8¹²⁴ [i]