MinT - Best Known (148−103, 148, s)-Nets in Base 9

Best Known (148−103, 148, s)-Nets in Base 9

(148−103, 148, 81)-Net over F₉ — Constructive and digital

Digital (45, 148, 81)-net over F₉, using

t-expansion [i] based on digital (32, 148, 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]

(148−103, 148, 147)-Net over F₉ — Digital

Digital (45, 148, 147)-net over F₉, using

t-expansion [i] based on digital (43, 148, 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]

(148−103, 148, 1365)-Net in Base 9 — Upper bound on s

There is no (45, 148, 1366)-net in base 9, because

1 times m-reduction [i] would yield (45, 147, 1366)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 188 222505 259289 128713 348642 481279 571091 407089 997811 496012 768708 605112 515951 836739 235011 132922 374064 237443 854605 909926 167693 406608 944118 901969 > 9¹⁴⁷ [i]