MinT - Best Known (65−22, 65, s)-Nets in Base 9

Best Known (65−22, 65, s)-Nets in Base 9

Digital (43, 65, 344)-net over F₉, using

7 times m-reduction [i] based on digital (43, 72, 344)-net over F₉, using
- trace code for nets [i] based on digital (7, 36, 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 (43, 65, 986)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9⁶⁵, 986, F₉, 22) (dual of [986, 921, 23]-code), using
- 920 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (3, 2, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 9 times 0, 1, 10 times 0, 1, 11 times 0, 1, 13 times 0, 1, 14 times 0, 1, 16 times 0, 1, 18 times 0, 1, 21 times 0, 1, 23 times 0, 1, 25 times 0, 1, 29 times 0, 1, 32 times 0, 1, 36 times 0, 1, 40 times 0, 1, 44 times 0, 1, 50 times 0, 1, 55 times 0, 1, 62 times 0, 1, 69 times 0, 1, 76 times 0, 1, 86 times 0, 1, 95 times 0) [i] based on linear OA(9²², 23, F₉, 22) (dual of [23, 1, 23]-code or 23-arc in PG(21,9)), using
  - dual of repetition code with length 23 [i]

There is no (43, 65, 267067)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 106 113509 656717 336690 945582 651471 008005 585387 477592 367933 196745 > 9⁶⁵ [i]