MinT - Best Known (124−79, 124, s)-Nets in Base 9

Best Known (124−79, 124, s)-Nets in Base 9

(124−79, 124, 81)-Net over F₉ — Constructive and digital

Digital (45, 124, 81)-net over F₉, using

t-expansion [i] based on digital (32, 124, 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]

(124−79, 124, 147)-Net over F₉ — Digital

Digital (45, 124, 147)-net over F₉, using

t-expansion [i] based on digital (43, 124, 147)-net over F₉, using
- net from sequence [i] based on digital (43, 146)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
    - a curve from the manYPoints database [i]

(124−79, 124, 1943)-Net in Base 9 — Upper bound on s

There is no (45, 124, 1944)-net in base 9, because

1 times m-reduction [i] would yield (45, 123, 1944)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2377 376518 792729 310126 295277 639042 418010 128578 572824 450258 180034 202586 393108 350475 752004 660336 662294 952474 187162 490945 > 9¹²³ [i]