MinT - Best Known (75, 75+75, s)-Nets in Base 9

Best Known (75, 75+75, s)-Nets in Base 9

(75, 75+75, 165)-Net over F₉ — Constructive and digital

Digital (75, 150, 165)-net over F₉, using

t-expansion [i] based on digital (64, 150, 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]

(75, 75+75, 277)-Net over F₉ — Digital

Digital (75, 150, 277)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(75, 75+75, 12729)-Net in Base 9 — Upper bound on s

There is no (75, 150, 12730)-net in base 9, because

1 times m-reduction [i] would yield (75, 149, 12730)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15232 197715 270915 149988 102386 983034 724570 957836 857510 878821 092547 437787 882786 083107 863724 416404 021467 634731 474516 713014 827507 715823 976411 222161 > 9¹⁴⁹ [i]