MinT - Best Known (22, 36, s)-Nets in Base 8

Best Known (22, 36, s)-Nets in Base 8

Digital (22, 36, 208)-net over F₈, using

2 times m-reduction [i] based on digital (22, 38, 208)-net over F₈, using
- trace code for nets [i] based on digital (3, 19, 104)-net over F₆₄, using
  - net from sequence [i] based on digital (3, 103)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 104, using
      - a function field by SÃ©mirat [i]

Digital (22, 36, 265)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8³⁶, 265, F₈, 14) (dual of [265, 229, 15]-code), using
- 37 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 9 times 0, 1, 26 times 0) [i] based on linear OA(8³⁴, 226, F₈, 14) (dual of [226, 192, 15]-code), using
  - trace code [i] based on linear OA(64¹⁷, 113, F₆₄, 14) (dual of [113, 96, 15]-code), using
    - extended algebraic-geometric code AG_e(F,98P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
      - a curve from the manYPoints database [i]

(22, 36, 300)-net in base 8, using

There is no (22, 36, 21292)-net in base 8, because

the generalized Rao bound for nets shows that 8^mÂ â‰¥ 324 595110 937714 422969 860182 732814 > 8³⁶ [i]