MinT - Best Known (88−53, 88, s)-Nets in Base 9

Best Known (88−53, 88, s)-Nets in Base 9

(88−53, 88, 81)-Net over F₉ — Constructive and digital

Digital (35, 88, 81)-net over F₉, using

t-expansion [i] based on digital (32, 88, 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]

(88−53, 88, 128)-Net over F₉ — Digital

Digital (35, 88, 128)-net over F₉, using

t-expansion [i] based on digital (33, 88, 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]

(88−53, 88, 2041)-Net in Base 9 — Upper bound on s

There is no (35, 88, 2042)-net in base 9, because

1 times m-reduction [i] would yield (35, 87, 2042)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 105373 695433 898835 783874 484145 659286 716005 506178 837745 672341 590656 984770 527324 904929 > 9⁸⁷ [i]