MinT - Best Known (144−102, 144, s)-Nets in Base 8

Best Known (144−102, 144, s)-Nets in Base 8

(144−102, 144, 98)-Net over F₈ — Constructive and digital

Digital (42, 144, 98)-net over F₈, using

t-expansion [i] based on digital (37, 144, 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]

(144−102, 144, 129)-Net over F₈ — Digital

Digital (42, 144, 129)-net over F₈, using

t-expansion [i] based on digital (38, 144, 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]

(144−102, 144, 974)-Net in Base 8 — Upper bound on s

There is no (42, 144, 975)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 11569 679402 677117 953956 664134 966783 147063 082519 248195 971975 064700 963094 154934 087615 980601 521494 910277 893669 633732 533379 591144 291792 > 8¹⁴⁴ [i]