MinT - Best Known (69, 99, s)-Nets in Base 9

Best Known (69, 99, s)-Nets in Base 9

Digital (69, 99, 740)-net over F₉, using

7 times m-reduction [i] based on digital (69, 106, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 53, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

Digital (69, 99, 2655)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁹⁹, 2655, F₉, 30) (dual of [2655, 2556, 31]-code), using
- 2555 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (5, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 0, 1, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 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, 10 times 0, 1, 10 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 19 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 34 times 0, 1, 37 times 0, 1, 41 times 0, 1, 43 times 0, 1, 47 times 0, 1, 52 times 0, 1, 55 times 0, 1, 60 times 0, 1, 65 times 0, 1, 69 times 0, 1, 76 times 0, 1, 82 times 0, 1, 88 times 0, 1, 95 times 0, 1, 103 times 0, 1, 112 times 0, 1, 120 times 0, 1, 130 times 0, 1, 140 times 0, 1, 152 times 0, 1, 163 times 0, 1, 177 times 0, 1, 191 times 0) [i] based on linear OA(9³⁰, 31, F₉, 30) (dual of [31, 1, 31]-code or 31-arc in PG(29,9)), using
  - dual of repetition code with length 31 [i]

There is no (69, 99, 1594685)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29512 777671 722734 685216 579629 360484 153105 113449 576660 969029 659018 939887 540990 237734 924363 885913 > 9⁹⁹ [i]