MinT - Best Known (165−127, 165, s)-Nets in Base 8

Best Known (165−127, 165, s)-Nets in Base 8

(165−127, 165, 98)-Net over F₈ — Constructive and digital

Digital (38, 165, 98)-net over F₈, using

t-expansion [i] based on digital (37, 165, 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]

(165−127, 165, 129)-Net over F₈ — Digital

Digital (38, 165, 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]

(165−127, 165, 739)-Net in Base 8 — Upper bound on s

There is no (38, 165, 740)-net in base 8, because

1 times m-reduction [i] would yield (38, 164, 740)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13321 701983 504446 745881 974662 266404 352573 701041 641511 811028 151169 930599 734279 998853 472860 684589 638344 669826 172243 423714 797666 191383 114974 682222 055792 > 8¹⁶⁴ [i]