MinT - Best Known (37, 142, s)-Nets in Base 9

Best Known (37, 142, s)-Nets in Base 9

(37, 142, 81)-Net over F₉ — Constructive and digital

Digital (37, 142, 81)-net over F₉, using

t-expansion [i] based on digital (32, 142, 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]

(37, 142, 128)-Net over F₉ — Digital

Digital (37, 142, 128)-net over F₉, using

t-expansion [i] based on digital (33, 142, 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]

(37, 142, 946)-Net in Base 9 — Upper bound on s

There is no (37, 142, 947)-net in base 9, because

1 times m-reduction [i] would yield (37, 141, 947)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 369 633360 083703 123606 441167 702104 250565 701343 703281 398901 031050 562019 918151 019179 627925 739201 747894 003923 534810 002936 537857 313511 945185 > 9¹⁴¹ [i]