MinT - Best Known (17, 29, s)-Nets in Base 8

Best Known (17, 29, s)-Nets in Base 8

Digital (17, 29, 160)-net over F₈, using

3 times m-reduction [i] based on digital (17, 32, 160)-net over F₈, using
- trace code for nets [i] based on digital (1, 16, 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 (17, 29, 198)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8²⁹, 198, F₈, 12) (dual of [198, 169, 13]-code), using
- 3 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 0, 0) [i] based on linear OA(8²⁸, 194, F₈, 12) (dual of [194, 166, 13]-code), using
  - trace code [i] based on linear OA(64¹⁴, 97, F₆₄, 12) (dual of [97, 83, 13]-code), using
    - extended algebraic-geometric code AG_e(F,84P) [i] based on function field F/F₆₄ with g(F) = 2 and N(F) ≥ 97, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

(17, 29, 258)-net in base 8, using

There is no (17, 29, 9907)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 154 807313 309305 810086 071020 > 8²⁹ [i]