MinT - Best Known (131−88, 131, s)-Nets in Base 9

Best Known (131−88, 131, s)-Nets in Base 9

(131−88, 131, 81)-Net over F₉ — Constructive and digital

Digital (43, 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]

(131−88, 131, 147)-Net over F₉ — Digital

Digital (43, 131, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(131−88, 131, 1468)-Net in Base 9 — Upper bound on s

There is no (43, 131, 1469)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 101516 993173 207580 735876 439163 298589 158733 276402 595056 276493 952258 256731 282119 084496 329329 513679 971191 148960 850490 744644 796769 > 9¹³¹ [i]