MinT - Best Known (35, 35+75, s)-Nets in Base 9

Best Known (35, 35+75, s)-Nets in Base 9

(35, 35+75, 81)-Net over F₉ — Constructive and digital

Digital (35, 110, 81)-net over F₉, using

t-expansion [i] based on digital (32, 110, 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+75, 128)-Net over F₉ — Digital

Digital (35, 110, 128)-net over F₉, using

t-expansion [i] based on digital (33, 110, 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+75, 1163)-Net in Base 9 — Upper bound on s

There is no (35, 110, 1164)-net in base 9, because

1 times m-reduction [i] would yield (35, 109, 1164)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 105 556574 550161 554946 657552 011380 556493 843758 713344 703190 133088 393440 074059 147743 340742 975729 090981 371105 > 9¹⁰⁹ [i]