MinT - Best Known (131−84, 131, s)-Nets in Base 9

Best Known (131−84, 131, s)-Nets in Base 9

(131−84, 131, 81)-Net over F₉ — Constructive and digital

Digital (47, 131, 81)-net over F₉, using

t-expansion [i] based on digital (32, 131, 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]

(131−84, 131, 162)-Net over F₉ — Digital

Digital (47, 131, 162)-net over F₉, using

t-expansion [i] based on digital (46, 131, 162)-net over F₉, using
- net from sequence [i] based on digital (46, 161)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 46 and N(F) ≥ 162, using
    - a curve from the manYPoints database [i]

(131−84, 131, 1928)-Net in Base 9 — Upper bound on s

There is no (47, 131, 1929)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101626 906304 051180 688093 090837 993402 280858 870596 383369 699473 940789 072678 053058 796677 840076 679853 782589 609760 652403 438997 150225 > 9¹³¹ [i]