MinT - Best Known (22, 22+15, s)-Nets in Base 9

Best Known (22, 22+15, s)-Nets in Base 9

Digital (22, 37, 232)-net over F₉, using

3 times m-reduction [i] based on digital (22, 40, 232)-net over F₉, using
- trace code for nets [i] based on digital (2, 20, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]

Digital (22, 37, 279)-net over F₉, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(9³⁷, 279, F₉, 15) (dual of [279, 242, 16]-code), using
- 6 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 5 times 0) [i] based on linear OA(9³⁶, 272, F₉, 15) (dual of [272, 236, 16]-code), using
  - trace code [i] based on linear OA(81¹⁸, 136, F₈₁, 15) (dual of [136, 118, 16]-code), using
    - extended algebraic-geometric code AG_e(F,120P) [i] based on function field F/F₈₁ with g(F) = 3 and N(F) ≥ 136, using
      - a curve from the manYPoints database [i]

There is no (22, 37, 34144)-net in base 9, because

1 times m-reduction [i] would yield (22, 36, 34144)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 22529 167325 110668 081971 382280 849665 > 9³⁶ [i]