MinT - Best Known (141−100, 141, s)-Nets in Base 9

Best Known (141−100, 141, s)-Nets in Base 9

(141−100, 141, 81)-Net over F₉ — Constructive and digital

Digital (41, 141, 81)-net over F₉, using

t-expansion [i] based on digital (32, 141, 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]

(141−100, 141, 140)-Net over F₉ — Digital

Digital (41, 141, 140)-net over F₉, using

t-expansion [i] based on digital (39, 141, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(141−100, 141, 1164)-Net in Base 9 — Upper bound on s

There is no (41, 141, 1165)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 354 232162 145690 791988 397344 426671 219941 187334 714000 317355 432251 357901 284389 724494 505561 789152 295691 669658 173441 203812 812382 895813 527825 > 9¹⁴¹ [i]