MinT - Best Known (146−72, 146, s)-Nets in Base 9

Best Known (146−72, 146, s)-Nets in Base 9

(146−72, 146, 200)-Net over F₉ — Constructive and digital

Digital (74, 146, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 73, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(146−72, 146, 287)-Net over F₉ — Digital

Digital (74, 146, 287)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(146−72, 146, 13210)-Net in Base 9 — Upper bound on s

There is no (74, 146, 13211)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 20 911775 768914 725039 090673 198022 316214 471697 434403 261276 266194 438033 934820 170048 781915 471469 263487 884970 839981 590896 984622 698434 727644 167521 > 9¹⁴⁶ [i]