MinT - Best Known (144−56, 144, s)-Nets in Base 9

Best Known (144−56, 144, s)-Nets in Base 9

(144−56, 144, 740)-Net over F₉ — Constructive and digital

Digital (88, 144, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 72, 370)-net over F₈₁, using
- net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
    - a function field by GarcÃa and Quoos [i]

(144−56, 144, 853)-Net over F₉ — Digital

Digital (88, 144, 853)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−56, 144, 114125)-Net in Base 9 — Upper bound on s

There is no (88, 144, 114126)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 257607 589078 430689 557185 162456 754572 350258 728322 951856 951674 026364 304904 930303 598788 039493 023062 190791 666005 717811 247173 386259 120051 947201 > 9¹⁴⁴ [i]