MinT - Best Known (43, 43+28, s)-Nets in Base 8

Best Known (43, 43+28, s)-Nets in Base 8

Digital (43, 71, 354)-net over F₈, using

1 times m-reduction [i] based on digital (43, 72, 354)-net over F₈, using
- trace code for nets [i] based on digital (7, 36, 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 (43, 71, 384)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8⁷¹, 384, F₈, 28) (dual of [384, 313, 29]-code), using
- 59 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 10 times 0, 1, 21 times 0, 1, 25 times 0) [i] based on linear OA(8⁶⁸, 322, F₈, 28) (dual of [322, 254, 29]-code), using
  - trace code [i] based on linear OA(64³⁴, 161, F₆₄, 28) (dual of [161, 127, 29]-code), using
    - extended algebraic-geometric code AG_e(F,132P) [i] based on function field F/F₆₄ with g(F) = 6 and N(F) ≥ 161, using
      - a curve from the manYPoints database [i]

There is no (43, 71, 32825)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 13164 507094 941679 632588 564248 055666 524228 966662 577316 639501 851416 > 8⁷¹ [i]