MinT - Best Known (91−55, 91, s)-Nets in Base 9

Best Known (91−55, 91, s)-Nets in Base 9

(91−55, 91, 81)-Net over F₉ — Constructive and digital

Digital (36, 91, 81)-net over F₉, using

t-expansion [i] based on digital (32, 91, 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]

(91−55, 91, 128)-Net over F₉ — Digital

Digital (36, 91, 128)-net over F₉, using

t-expansion [i] based on digital (33, 91, 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]

(91−55, 91, 2054)-Net in Base 9 — Upper bound on s

There is no (36, 91, 2055)-net in base 9, because

1 times m-reduction [i] would yield (36, 90, 2055)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 76 774226 314736 176294 580553 188386 058417 182157 611360 169602 733659 283033 422515 526833 710825 > 9⁹⁰ [i]