MinT - Best Known (165−121, 165, s)-Nets in Base 8

Best Known (165−121, 165, s)-Nets in Base 8

(165−121, 165, 98)-Net over F₈ — Constructive and digital

Digital (44, 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]

(165−121, 165, 130)-Net over F₈ — Digital

Digital (44, 165, 130)-net over F₈, using

net from sequence [i] based on digital (44, 129)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 44 and N(F) ≥ 130, using
  - a curve from the manYPoints database [i]

(165−121, 165, 936)-Net in Base 8 — Upper bound on s

There is no (44, 165, 937)-net in base 8, because

1 times m-reduction [i] would yield (44, 164, 937)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13063 227254 180343 916358 696030 620937 903956 872533 366741 992926 773082 605707 726400 546634 439989 583096 720751 126116 629188 513600 803585 476551 824339 839332 098784 > 8¹⁶⁴ [i]