MinT - Best Known (124−58, 124, s)-Nets in Base 9

Best Known (124−58, 124, s)-Nets in Base 9

(124−58, 124, 300)-Net over F₉ — Constructive and digital

Digital (66, 124, 300)-net over F₉, using

trace code for nets [i] based on digital (4, 62, 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]

(124−58, 124, 314)-Net over F₉ — Digital

Digital (66, 124, 314)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(124−58, 124, 17530)-Net in Base 9 — Upper bound on s

There is no (66, 124, 17531)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 21189 306867 236197 835921 526247 944355 018788 106004 300779 768656 316984 395411 265545 940371 505034 043045 508582 013041 757227 245177 > 9¹²⁴ [i]