MinT - Best Known (171−134, 171, s)-Nets in Base 8

Best Known (171−134, 171, s)-Nets in Base 8

(171−134, 171, 98)-Net over F₈ — Constructive and digital

Digital (37, 171, 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]

(171−134, 171, 121)-Net over F₈ — Digital

Digital (37, 171, 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]

(171−134, 171, 701)-Net in Base 8 — Upper bound on s

There is no (37, 171, 702)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 28133 184806 809248 095527 001798 977450 408964 312699 234557 101933 465586 636288 264711 371776 683276 019763 040366 705357 439830 401335 490180 958128 035653 239234 334748 573684 > 8¹⁷¹ [i]