MinT - Best Known (53, 87, s)-Nets in Base 8

Best Known (53, 87, s)-Nets in Base 8

Digital (53, 87, 354)-net over F₈, using

5 times m-reduction [i] based on digital (53, 92, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 46, 177)-net over F₆₄, using
  - net from sequence [i] based on digital (7, 176)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 7 and N(F) ≥ 177, using
      - a function field by GarcÃa and Quoos [i]

Digital (53, 87, 469)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8⁸⁷, 469, F₈, 34) (dual of [469, 382, 35]-code), using
- 381 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (6, 2, 2, 1, 1, 1, 1, 1, 0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 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, 5 times 0, 1, 5 times 0, 1, 5 times 0, 1, 6 times 0, 1, 6 times 0, 1, 7 times 0, 1, 8 times 0, 1, 8 times 0, 1, 8 times 0, 1, 10 times 0, 1, 10 times 0, 1, 11 times 0, 1, 12 times 0, 1, 12 times 0, 1, 14 times 0, 1, 15 times 0, 1, 15 times 0, 1, 17 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0) [i] based on linear OA(8³⁴, 35, F₈, 34) (dual of [35, 1, 35]-code or 35-arc in PG(33,8)), using
  - dual of repetition code with length 35 [i]

There is no (53, 87, 42899)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 3 706759 894691 766251 725366 491562 741151 718355 447362 247281 229287 143394 825555 726262 > 8⁸⁷ [i]