MinT - Best Known (122−75, 122, s)-Nets in Base 9

Best Known (122−75, 122, s)-Nets in Base 9

(122−75, 122, 81)-Net over F₉ — Constructive and digital

Digital (47, 122, 81)-net over F₉, using

t-expansion [i] based on digital (32, 122, 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]

(122−75, 122, 162)-Net over F₉ — Digital

Digital (47, 122, 162)-net over F₉, using

t-expansion [i] based on digital (46, 122, 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]

(122−75, 122, 2395)-Net in Base 9 — Upper bound on s

There is no (47, 122, 2396)-net in base 9, because

1 times m-reduction [i] would yield (47, 121, 2396)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29 323527 760581 153027 729581 690441 194326 085780 282908 216378 855883 512144 929880 422553 057085 482585 199971 471084 971377 258849 > 9¹²¹ [i]