MinT - Best Known (144−68, 144, s)-Nets in Base 9

Best Known (144−68, 144, s)-Nets in Base 9

(144−68, 144, 300)-Net over F₉ — Constructive and digital

Digital (76, 144, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 72, 150)-net over F₈₁, using
- net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
    - a function field by SÃ©mirat [i]

(144−68, 144, 342)-Net over F₉ — Digital

Digital (76, 144, 342)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(144−68, 144, 18595)-Net in Base 9 — Upper bound on s

There is no (76, 144, 18596)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 258000 777164 975587 428348 519126 698689 629828 232735 640612 399476 608356 376621 656151 548190 610993 456601 237347 970240 310041 927869 391029 289180 011713 > 9¹⁴⁴ [i]