MinT - Best Known (140−73, 140, s)-Nets in Base 9

Best Known (140−73, 140, s)-Nets in Base 9

(140−73, 140, 165)-Net over F₉ — Constructive and digital

Digital (67, 140, 165)-net over F₉, using

t-expansion [i] based on digital (64, 140, 165)-net over F₉, using
- net from sequence [i] based on digital (64, 164)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 64 and N(F) ≥ 165, using
    - T₄ from the second tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(140−73, 140, 218)-Net over F₉ — Digital

Digital (67, 140, 218)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(140−73, 140, 8609)-Net in Base 9 — Upper bound on s

There is no (67, 140, 8610)-net in base 9, because

1 times m-reduction [i] would yield (67, 139, 8610)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 372059 279461 320131 852620 828214 491041 830505 358839 887080 392865 483364 829240 799786 812887 002334 099122 398613 845915 140401 194962 428577 838785 > 9¹³⁹ [i]