MinT - Best Known (169−127, 169, s)-Nets in Base 8

Best Known (169−127, 169, s)-Nets in Base 8

(169−127, 169, 98)-Net over F₈ — Constructive and digital

Digital (42, 169, 98)-net over F₈, using

t-expansion [i] based on digital (37, 169, 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]

(169−127, 169, 129)-Net over F₈ — Digital

Digital (42, 169, 129)-net over F₈, using

t-expansion [i] based on digital (38, 169, 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]

(169−127, 169, 849)-Net in Base 8 — Upper bound on s

There is no (42, 169, 850)-net in base 8, because

1 times m-reduction [i] would yield (42, 168, 850)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 54 837994 100655 305941 482358 205808 674532 077900 805767 851208 614511 875523 775939 139545 360367 900475 284374 333868 021608 660589 068050 078832 885210 148464 688885 263072 > 8¹⁶⁸ [i]