MinT - Best Known (141−95, 141, s)-Nets in Base 9

Best Known (141−95, 141, s)-Nets in Base 9

(141−95, 141, 81)-Net over F₉ — Constructive and digital

Digital (46, 141, 81)-net over F₉, using

t-expansion [i] based on digital (32, 141, 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]

(141−95, 141, 162)-Net over F₉ — Digital

Digital (46, 141, 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]

(141−95, 141, 1568)-Net in Base 9 — Upper bound on s

There is no (46, 141, 1569)-net in base 9, because

1 times m-reduction [i] would yield (46, 140, 1569)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 39 549088 900065 502409 341584 700440 458891 472987 719900 729096 981269 854600 927755 091784 102211 230048 248891 795088 192325 231652 945227 532465 264825 > 9¹⁴⁰ [i]