MinT - Best Known (155−117, 155, s)-Nets in Base 8

Best Known (155−117, 155, s)-Nets in Base 8

(155−117, 155, 98)-Net over F₈ — Constructive and digital

Digital (38, 155, 98)-net over F₈, using

t-expansion [i] based on digital (37, 155, 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]

(155−117, 155, 129)-Net over F₈ — Digital

Digital (38, 155, 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]

(155−117, 155, 765)-Net in Base 8 — Upper bound on s

There is no (38, 155, 766)-net in base 8, because

1 times m-reduction [i] would yield (38, 154, 766)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 12 461114 196807 261320 183731 634735 037773 236009 264161 269515 162696 119905 882450 993716 299819 052665 874487 043337 437789 325896 178468 691872 959243 380042 > 8¹⁵⁴ [i]