MinT - Best Known (39, 122, s)-Nets in Base 8

Best Known (39, 122, s)-Nets in Base 8

(39, 122, 98)-Net over F₈ — Constructive and digital

Digital (39, 122, 98)-net over F₈, using

t-expansion [i] based on digital (37, 122, 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, 122, 129)-Net over F₈ — Digital

Digital (39, 122, 129)-net over F₈, using

t-expansion [i] based on digital (38, 122, 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, 122, 1041)-Net in Base 8 — Upper bound on s

There is no (39, 122, 1042)-net in base 8, because

1 times m-reduction [i] would yield (39, 121, 1042)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 19 519909 687381 284563 228041 817907 486595 855397 750095 807110 010668 342238 251916 913960 414424 211309 342167 941841 950400 > 8¹²¹ [i]