MinT - Best Known (44, 44+106, s)-Nets in Base 9

Best Known (44, 44+106, s)-Nets in Base 9

(44, 44+106, 81)-Net over F₉ — Constructive and digital

Digital (44, 150, 81)-net over F₉, using

t-expansion [i] based on digital (32, 150, 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]

(44, 44+106, 147)-Net over F₉ — Digital

Digital (44, 150, 147)-net over F₉, using

t-expansion [i] based on digital (43, 150, 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]

(44, 44+106, 1259)-Net in Base 9 — Upper bound on s

There is no (44, 150, 1260)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 136977 984679 892486 584654 116672 639338 452296 400610 604329 984787 683546 450839 125533 808527 553122 171107 195620 887720 378388 329237 311376 027247 163496 699361 > 9¹⁵⁰ [i]