MinT - Best Known (104−50, 104, s)-Nets in Base 9

Best Known (104−50, 104, s)-Nets in Base 9

(104−50, 104, 232)-Net over F₉ — Constructive and digital

Digital (54, 104, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 52, 116)-net over F₈₁, using
- net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
    - a function field by SÃ©mirat [i]

(104−50, 104, 241)-Net over F₉ — Digital

Digital (54, 104, 241)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(104−50, 104, 11847)-Net in Base 9 — Upper bound on s

There is no (54, 104, 11848)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1744 120156 202469 966116 310764 697452 207705 166379 313219 453390 648520 710935 138508 790171 167390 403789 165633 > 9¹⁰⁴ [i]