MinT - Best Known (79, 127, s)-Nets in Base 9

Best Known (79, 127, s)-Nets in Base 9

Digital (79, 127, 448)-net over F₉, using

5 times m-reduction [i] based on digital (79, 132, 448)-net over F₉, using
- trace code for nets [i] based on digital (13, 66, 224)-net over F₈₁, using
  - net from sequence [i] based on digital (13, 223)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 13 and N(F) ≥ 224, using
      - a function field by SÃ©mirat [i]

Digital (79, 127, 894)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9¹²⁷, 894, F₉, 48) (dual of [894, 767, 49]-code), using
- 766 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (7, 3, 2, 1, 2, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 9 times 0, 1, 9 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 13 times 0, 1, 13 times 0, 1, 15 times 0, 1, 15 times 0, 1, 16 times 0, 1, 16 times 0, 1, 18 times 0, 1, 19 times 0, 1, 19 times 0, 1, 21 times 0, 1, 22 times 0, 1, 23 times 0, 1, 24 times 0, 1, 25 times 0, 1, 27 times 0, 1, 28 times 0, 1, 29 times 0, 1, 31 times 0, 1, 33 times 0, 1, 34 times 0, 1, 36 times 0, 1, 38 times 0) [i] based on linear OA(9⁴⁸, 49, F₉, 48) (dual of [49, 1, 49]-code or 49-arc in PG(47,9)), using
  - dual of repetition code with length 49 [i]

There is no (79, 127, 137329)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 15 447159 699928 893482 100792 901616 413787 531389 431861 263041 061163 125125 993392 926890 409984 318364 302441 887231 821594 071825 797569 > 9¹²⁷ [i]