MinT - Best Known (15−6, 15, s)-Nets in Base 8

Best Known (15−6, 15, s)-Nets in Base 8

Digital (9, 15, 160)-net over F₈, using

1 times m-reduction [i] based on digital (9, 16, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 8, 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 (9, 15, 203)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8¹⁵, 203, F₈, 6) (dual of [203, 188, 7]-code), using
- 40 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 39 times 0) [i] based on linear OA(8¹⁴, 162, F₈, 6) (dual of [162, 148, 7]-code), using
  - trace code [i] based on linear OA(64⁷, 81, F₆₄, 6) (dual of [81, 74, 7]-code), using
    - extended algebraic-geometric code AG_e(F,74P) [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]

(9, 15, 258)-net in base 8, using

There is no (9, 15, 8505)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 35 187193 849816 > 8¹⁵ [i]