MinT - Best Known (125−78, 125, s)-Nets in Base 9

Best Known (125−78, 125, s)-Nets in Base 9

(125−78, 125, 81)-Net over F₉ — Constructive and digital

Digital (47, 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]

(125−78, 125, 162)-Net over F₉ — Digital

Digital (47, 125, 162)-net over F₉, using

t-expansion [i] based on digital (46, 125, 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]

(125−78, 125, 2178)-Net in Base 9 — Upper bound on s

There is no (47, 125, 2179)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 193618 326019 227563 965838 799761 319092 261914 859705 707072 467980 501536 644104 867060 466049 367182 184055 781000 947084 740797 936425 > 9¹²⁵ [i]