MinT - Best Known (70, 70+79, s)-Nets in Base 9

Best Known (70, 70+79, s)-Nets in Base 9

(70, 70+79, 165)-Net over F₉ — Constructive and digital

Digital (70, 149, 165)-net over F₉, using

t-expansion [i] based on digital (64, 149, 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]

(70, 70+79, 215)-Net over F₉ — Digital

Digital (70, 149, 215)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(70, 70+79, 8021)-Net in Base 9 — Upper bound on s

There is no (70, 149, 8022)-net in base 9, because

1 times m-reduction [i] would yield (70, 148, 8022)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 1691 369900 656707 211777 308341 203446 760989 256418 425744 050235 007955 771675 640818 337081 257455 317940 499364 165631 955089 307778 821101 158032 219684 338961 > 9¹⁴⁸ [i]