MinT - Best Known (47, 71, s)-Nets in Base 9

Best Known (47, 71, s)-Nets in Base 9

Digital (47, 71, 344)-net over F₉, using

9 times m-reduction [i] based on digital (47, 80, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 40, 172)-net over F₈₁, using
  - net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
      - a function field by SÃ©mirat [i]

Digital (47, 71, 1052)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁷¹, 1052, F₉, 24) (dual of [1052, 981, 25]-code), using
- 980 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (4, 2, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 6 times 0, 1, 6 times 0, 1, 8 times 0, 1, 8 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 28 times 0, 1, 31 times 0, 1, 35 times 0, 1, 38 times 0, 1, 42 times 0, 1, 46 times 0, 1, 52 times 0, 1, 57 times 0, 1, 62 times 0, 1, 69 times 0, 1, 77 times 0, 1, 84 times 0, 1, 93 times 0) [i] based on linear OA(9²⁴, 25, F₉, 24) (dual of [25, 1, 25]-code or 25-arc in PG(23,9)), using
  - dual of repetition code with length 25 [i]

There is no (47, 71, 292548)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 56 394036 141611 821991 223640 068686 544449 253565 782412 646320 071129 337473 > 9⁷¹ [i]