MinT - Best Known (170−127, 170, s)-Nets in Base 8

Best Known (170−127, 170, s)-Nets in Base 8

(170−127, 170, 98)-Net over F₈ — Constructive and digital

Digital (43, 170, 98)-net over F₈, using

t-expansion [i] based on digital (37, 170, 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]

(170−127, 170, 129)-Net over F₈ — Digital

Digital (43, 170, 129)-net over F₈, using

t-expansion [i] based on digital (38, 170, 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]

(170−127, 170, 879)-Net in Base 8 — Upper bound on s

There is no (43, 170, 880)-net in base 8, because

1 times m-reduction [i] would yield (43, 169, 880)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 443 802701 100035 082020 016983 668383 582992 386784 025449 094964 146319 298136 226486 706604 777671 044164 116993 422727 916210 176773 106814 985919 630727 979851 035457 859836 > 8¹⁶⁹ [i]