MinT - Best Known (22, 37, s)-Nets in Base 8

Best Known (22, 37, s)-Nets in Base 8

Digital (22, 37, 208)-net over F₈, using

1 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, 37, 233)-net over F₈, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(8³⁷, 233, F₈, 15) (dual of [233, 196, 16]-code), using
- 6 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 5 times 0) [i] based on linear OA(8³⁶, 226, F₈, 15) (dual of [226, 190, 16]-code), using
  - trace code [i] based on linear OA(64¹⁸, 113, F₆₄, 15) (dual of [113, 95, 16]-code), using
    - extended algebraic-geometric code AG_e(F,97P) [i] based on function field F/F₆₄ with g(F) = 3 and N(F) ≥ 113, using
      - a curve from the manYPoints database [i]

(22, 37, 258)-net in base 8, using

There is no (22, 37, 21292)-net in base 8, because

1 times m-reduction [i] would yield (22, 36, 21292)-net in base 8, but
- the generalized Rao bound for nets shows that 8^mÂ â‰¥ 324 595110 937714 422969 860182 732814 > 8³⁶ [i]