MinT - Best Known (39, 162, s)-Nets in Base 8

Best Known (39, 162, s)-Nets in Base 8

(39, 162, 98)-Net over F₈ — Constructive and digital

Digital (39, 162, 98)-net over F₈, using

t-expansion [i] based on digital (37, 162, 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]

(39, 162, 129)-Net over F₈ — Digital

Digital (39, 162, 129)-net over F₈, using

t-expansion [i] based on digital (38, 162, 129)-net over F₈, using
- net from sequence [i] based on digital (38, 128)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 38 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(39, 162, 775)-Net in Base 8 — Upper bound on s

There is no (39, 162, 776)-net in base 8, because

1 times m-reduction [i] would yield (39, 161, 776)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 25 062662 036323 029282 566000 398947 226888 873544 472230 315735 734338 667259 199466 730690 349070 877283 069477 522434 052869 989420 656078 413154 822377 861093 394912 > 8¹⁶¹ [i]