MinT - Best Known (38, 38+69, s)-Nets in Base 8

Best Known (38, 38+69, s)-Nets in Base 8

(38, 38+69, 98)-Net over F₈ — Constructive and digital

Digital (38, 107, 98)-net over F₈, using

t-expansion [i] based on digital (37, 107, 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]

(38, 38+69, 129)-Net over F₈ — Digital

Digital (38, 107, 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]

(38, 38+69, 1243)-Net in Base 8 — Upper bound on s

There is no (38, 107, 1244)-net in base 8, because

1 times m-reduction [i] would yield (38, 106, 1244)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 545927 813525 345036 223174 946984 166424 050480 378279 989705 773330 646189 445878 408873 613008 708554 006402 > 8¹⁰⁶ [i]