MinT - Best Known (127−83, 127, s)-Nets in Base 8

Best Known (127−83, 127, s)-Nets in Base 8

(127−83, 127, 98)-Net over F₈ — Constructive and digital

Digital (44, 127, 98)-net over F₈, using

t-expansion [i] based on digital (37, 127, 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]

(127−83, 127, 130)-Net over F₈ — Digital

Digital (44, 127, 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]

(127−83, 127, 1348)-Net in Base 8 — Upper bound on s

There is no (44, 127, 1349)-net in base 8, because

1 times m-reduction [i] would yield (44, 126, 1349)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 618365 856448 574414 312486 544030 867184 609128 091880 069880 314790 842222 472190 000396 006489 976832 433619 814597 301701 303456 > 8¹²⁶ [i]