MinT - Best Known (11, 19, s)-Nets in Base 8

Best Known (11, 19, s)-Nets in Base 8

Digital (11, 19, 160)-net over F₈, using

1 times m-reduction [i] based on digital (11, 20, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 10, 80)-net over F₆₄, using
  - net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
      - a function field by SÃ©mirat [i]

Digital (11, 19, 169)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹⁹, 169, F₈, 8) (dual of [169, 150, 9]-code), using
- 6 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 5 times 0) [i] based on linear OA(8¹⁸, 162, F₈, 8) (dual of [162, 144, 9]-code), using
  - trace code [i] based on linear OA(64⁹, 81, F₆₄, 8) (dual of [81, 72, 9]-code), using
    - extended algebraic-geometric code AG_e(F,72P) [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 81, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

There is no (11, 19, 6159)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 144147 070361 954633 > 8¹⁹ [i]