MinT - Best Known (43, 67, s)-Nets in Base 5

Best Known (43, 67, s)-Nets in Base 5

Digital (43, 67, 208)-net over F₅, using

1 times m-reduction [i] based on digital (43, 68, 208)-net over F₅, using
- trace code for nets [i] based on digital (9, 34, 104)-net over F₂₅, using
  - net from sequence [i] based on digital (9, 103)-sequence over F₂₅, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 9 and N(F) ≥ 104, using
      - a function field by GarcÃa and Quoos [i]

Digital (43, 67, 268)-net over F₅, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(5⁶⁷, 268, F₅, 24) (dual of [268, 201, 25]-code), using
- 200 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 2, 2, 1, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0) [i] based on linear OA(5²⁴, 25, F₅, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,5)), using
  - dual of repetition code with length 25 [i]

There is no (43, 67, 10557)-net in base 5, because

the generalized Rao bound for nets shows that 5^mÂ â‰¥ 67773 879087 436145 967001 839209 890864 589108 796625 > 5⁶⁷ [i]