MinT - Best Known (131−85, 131, s)-Nets in Base 9

Best Known (131−85, 131, s)-Nets in Base 9

(131−85, 131, 81)-Net over F₉ — Constructive and digital

Digital (46, 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]

(131−85, 131, 162)-Net over F₉ — Digital

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]

(131−85, 131, 1829)-Net in Base 9 — Upper bound on s

There is no (46, 131, 1830)-net in base 9, because

1 times m-reduction [i] would yield (46, 130, 1830)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11452 338433 467512 935254 285944 349211 328177 473399 873148 605969 543616 407502 216985 083889 425309 014759 756729 617297 961163 726877 003297 > 9¹³⁰ [i]