MinT - Best Known (35, 35+93, s)-Nets in Base 9

Best Known (35, 35+93, s)-Nets in Base 9

(35, 35+93, 81)-Net over F₉ — Constructive and digital

Digital (35, 128, 81)-net over F₉, using

t-expansion [i] based on digital (32, 128, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(35, 35+93, 128)-Net over F₉ — Digital

Digital (35, 128, 128)-net over F₉, using

t-expansion [i] based on digital (33, 128, 128)-net over F₉, using
- net from sequence [i] based on digital (33, 127)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
    - a curve from the manYPoints database [i]

(35, 35+93, 941)-Net in Base 9 — Upper bound on s

There is no (35, 128, 942)-net in base 9, because

1 times m-reduction [i] would yield (35, 127, 942)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 606802 033419 624728 845351 008710 131689 205773 905980 220136 590911 854924 836953 355867 186204 919199 521808 201740 380255 354039 252705 > 9¹²⁷ [i]