MinT - Best Known (35, 35+81, s)-Nets in Base 9

Best Known (35, 35+81, s)-Nets in Base 9

(35, 35+81, 81)-Net over F₉ — Constructive and digital

Digital (35, 116, 81)-net over F₉, using

t-expansion [i] based on digital (32, 116, 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]

(35, 35+81, 128)-Net over F₉ — Digital

Digital (35, 116, 128)-net over F₉, using

t-expansion [i] based on digital (33, 116, 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]

(35, 35+81, 1067)-Net in Base 9 — Upper bound on s

There is no (35, 116, 1068)-net in base 9, because

1 times m-reduction [i] would yield (35, 115, 1068)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 55 752995 286742 311783 325611 212422 305031 137975 469971 693534 769439 141921 949508 105109 730385 345494 034404 431819 174145 > 9¹¹⁵ [i]