MinT - Best Known (166−129, 166, s)-Nets in Base 8

Best Known (166−129, 166, s)-Nets in Base 8

(166−129, 166, 98)-Net over F₈ — Constructive and digital

Digital (37, 166, 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]

(166−129, 166, 121)-Net over F₈ — Digital

Digital (37, 166, 121)-net over F₈, using

net from sequence [i] based on digital (37, 120)-sequence over F₈, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 37 and N(F) ≥ 121, using
  - a curve from the manYPoints database [i]

(166−129, 166, 710)-Net in Base 8 — Upper bound on s

There is no (37, 166, 711)-net in base 8, because

1 times m-reduction [i] would yield (37, 165, 711)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 105565 929822 393859 524960 553456 824285 699021 053038 832723 310070 206544 671959 692700 520131 638886 679699 820504 792039 420616 292859 301698 297670 311829 571821 631479 > 8¹⁶⁵ [i]