MinT - Best Known (84, 132, s)-Nets in Base 9

Best Known (84, 132, s)-Nets in Base 9

Digital (84, 132, 740)-net over F₉, using

4 times m-reduction [i] based on digital (84, 136, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 68, 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 (84, 132, 1123)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9¹³², 1123, F₉, 48) (dual of [1123, 991, 49]-code), using
- 990 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, 1, 39 times 0, 1, 42 times 0, 1, 43 times 0, 1, 46 times 0, 1, 49 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 (84, 132, 217059)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912047 405452 471386 576083 031827 341437 149576 817810 274491 366655 536740 875318 691141 753159 384905 946442 188749 858331 696722 382023 776321 > 9¹³² [i]