MinT - Best Known (106−68, 106, s)-Nets in Base 9

Best Known (106−68, 106, s)-Nets in Base 9

(106−68, 106, 81)-Net over F₉ — Constructive and digital

Digital (38, 106, 81)-net over F₉, using

t-expansion [i] based on digital (32, 106, 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]

(106−68, 106, 128)-Net over F₉ — Digital

Digital (38, 106, 128)-net over F₉, using

t-expansion [i] based on digital (33, 106, 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]

(106−68, 106, 1576)-Net in Base 9 — Upper bound on s

There is no (38, 106, 1577)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 142384 943928 010700 870391 310862 856294 547786 464518 635079 647692 706923 383406 342550 257900 496955 260838 854353 > 9¹⁰⁶ [i]