MinT - Best Known (37, 37+122, s)-Nets in Base 8

Best Known (37, 37+122, s)-Nets in Base 8

(37, 37+122, 98)-Net over F₈ — Constructive and digital

Digital (37, 159, 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]

(37, 37+122, 121)-Net over F₈ — Digital

Digital (37, 159, 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]

(37, 37+122, 722)-Net in Base 8 — Upper bound on s

There is no (37, 159, 723)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 411609 002851 276756 604014 488140 905921 091677 459686 470003 975335 498420 524113 165819 636905 866592 678270 366787 649545 123312 833566 737094 064296 400169 771104 > 8¹⁵⁹ [i]