MinT - Best Known (118−74, 118, s)-Nets in Base 9

Best Known (118−74, 118, s)-Nets in Base 9

(118−74, 118, 81)-Net over F₉ — Constructive and digital

Digital (44, 118, 81)-net over F₉, using

t-expansion [i] based on digital (32, 118, 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]

(118−74, 118, 147)-Net over F₉ — Digital

Digital (44, 118, 147)-net over F₉, using

t-expansion [i] based on digital (43, 118, 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]

(118−74, 118, 2000)-Net in Base 9 — Upper bound on s

There is no (44, 118, 2001)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39977 478607 856612 467423 466574 175855 389329 674548 021602 177352 495535 295034 196663 124672 350530 662826 787044 103742 292009 > 9¹¹⁸ [i]