MinT - Best Known (140−68, 140, s)-Nets in Base 9

Best Known (140−68, 140, s)-Nets in Base 9

(140−68, 140, 232)-Net over F₉ — Constructive and digital

Digital (72, 140, 232)-net over F₉, using

trace code for nets [i] based on digital (2, 70, 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]

(140−68, 140, 296)-Net over F₉ — Digital

Digital (72, 140, 296)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−68, 140, 14354)-Net in Base 9 — Upper bound on s

There is no (72, 140, 14355)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 293731 979219 998064 681260 358397 129355 047269 938207 279603 016082 550820 713022 670393 328093 391776 593080 731505 002437 255180 739224 014268 771249 > 9¹⁴⁰ [i]