MinT - Best Known (67, 67+71, s)-Nets in Base 9

Best Known (67, 67+71, s)-Nets in Base 9

(67, 67+71, 165)-Net over F₉ — Constructive and digital

Digital (67, 138, 165)-net over F₉, using

t-expansion [i] based on digital (64, 138, 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]

(67, 67+71, 228)-Net over F₉ — Digital

Digital (67, 138, 228)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(67, 67+71, 9426)-Net in Base 9 — Upper bound on s

There is no (67, 138, 9427)-net in base 9, because

1 times m-reduction [i] would yield (67, 137, 9427)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 53875 740215 112376 960485 872142 330802 106894 383120 677984 625829 400606 192108 250617 029355 243533 172632 702552 939215 524072 739366 988326 537545 > 9¹³⁷ [i]