MinT - Best Known (37, 145, s)-Nets in Base 9

Best Known (37, 145, s)-Nets in Base 9

(37, 145, 81)-Net over F₉ — Constructive and digital

Digital (37, 145, 81)-net over F₉, using

t-expansion [i] based on digital (32, 145, 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, 145, 128)-Net over F₉ — Digital

Digital (37, 145, 128)-net over F₉, using

t-expansion [i] based on digital (33, 145, 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, 145, 923)-Net in Base 9 — Upper bound on s

There is no (37, 145, 924)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2 348343 383404 094863 791825 626448 421605 227235 305528 072737 267748 269796 527060 226929 759628 425727 682776 535522 730585 033974 113883 159959 252157 470145 > 9¹⁴⁵ [i]