MinT - Best Known (125−82, 125, s)-Nets in Base 9

Best Known (125−82, 125, s)-Nets in Base 9

(125−82, 125, 81)-Net over F₉ — Constructive and digital

Digital (43, 125, 81)-net over F₉, using

t-expansion [i] based on digital (32, 125, 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]

(125−82, 125, 147)-Net over F₉ — Digital

Digital (43, 125, 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]

(125−82, 125, 1612)-Net in Base 9 — Upper bound on s

There is no (43, 125, 1613)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 194655 568763 514334 903566 614006 072110 069332 775988 464584 347151 289382 796971 954860 296092 107604 383929 014532 241013 944648 223145 > 9¹²⁵ [i]