MinT - Best Known (52, 52+87, s)-Nets in Base 9

Best Known (52, 52+87, s)-Nets in Base 9

(52, 52+87, 81)-Net over F₉ — Constructive and digital

Digital (52, 139, 81)-net over F₉, using

t-expansion [i] based on digital (32, 139, 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]

(52, 52+87, 182)-Net over F₉ — Digital

Digital (52, 139, 182)-net over F₉, using

t-expansion [i] based on digital (50, 139, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(52, 52+87, 2410)-Net in Base 9 — Upper bound on s

There is no (52, 139, 2411)-net in base 9, because

1 times m-reduction [i] would yield (52, 138, 2411)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 488366 021360 337723 208420 941454 002508 730422 821355 999772 221469 010972 818134 598923 353900 773155 877459 639000 932823 347988 517565 618919 174985 > 9¹³⁸ [i]