MinT - Best Known (114−70, 114, s)-Nets in Base 8

Best Known (114−70, 114, s)-Nets in Base 8

(114−70, 114, 98)-Net over F₈ — Constructive and digital

Digital (44, 114, 98)-net over F₈, using

t-expansion [i] based on digital (37, 114, 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]

(114−70, 114, 130)-Net over F₈ — Digital

Digital (44, 114, 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]

(114−70, 114, 1714)-Net in Base 8 — Upper bound on s

There is no (44, 114, 1715)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 9 045861 827833 423871 511118 181918 126801 983806 806035 615075 252243 056450 706218 935463 569756 899229 138730 030968 > 8¹¹⁴ [i]