MinT - Best Known (29, 29+65, s)-Nets in Base 9

Best Known (29, 29+65, s)-Nets in Base 9

(29, 29+65, 78)-Net over F₉ — Constructive and digital

Digital (29, 94, 78)-net over F₉, using

t-expansion [i] based on digital (22, 94, 78)-net over F₉, using
- net from sequence [i] based on digital (22, 77)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 22 and N(F) ≥ 78, using
    - F₃ from the tower of function fields by GarcÃa and Stichtenoth over F₉ [i]

(29, 29+65, 110)-Net over F₉ — Digital

Digital (29, 94, 110)-net over F₉, using

t-expansion [i] based on digital (26, 94, 110)-net over F₉, using
- net from sequence [i] based on digital (26, 109)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 26 and N(F) ≥ 110, using
    - a curve from the manYPoints database [i]

(29, 29+65, 929)-Net in Base 9 — Upper bound on s

There is no (29, 94, 930)-net in base 9, because

1 times m-reduction [i] would yield (29, 93, 930)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 57125 257464 027341 001194 705237 846682 819967 847643 209918 878360 121023 053178 226337 863335 499265 > 9⁹³ [i]