MinT - Best Known (61, 61+88, s)-Nets in Base 9

Best Known (61, 61+88, s)-Nets in Base 9

(61, 61+88, 94)-Net over F₉ — Constructive and digital

Digital (61, 149, 94)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (4, 48, 30)-net over F₉, using
  - net from sequence [i] based on digital (4, 29)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 4 and N(F) ≥ 30, using
      - a function field by SÃ©mirat [i]
2. digital (13, 101, 64)-net over F₉, using
  - net from sequence [i] based on digital (13, 63)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
      - a function field by GarcÃa and Quoos [i]

(61, 61+88, 96)-Net in Base 9 — Constructive

(61, 149, 96)-net in base 9, using

1 times m-reduction [i] based on (61, 150, 96)-net in base 9, using
- base change [i] based on digital (11, 100, 96)-net over F₂₇, using
  - net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
      - an explicitly constructive algebraic function field [i]

(61, 61+88, 192)-Net over F₉ — Digital

Digital (61, 149, 192)-net over F₉, using

net from sequence [i] based on digital (61, 191)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 61 and N(F) ≥ 192, using
  - Drinfeld modules of rank 1 [i]

(61, 61+88, 3647)-Net in Base 9 — Upper bound on s

There is no (61, 149, 3648)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15218 847819 782876 984020 914610 354466 944812 165243 524153 786284 818066 254930 265787 200052 000754 647556 679866 203364 190401 821550 772083 452274 880864 954369 > 9¹⁴⁹ [i]