MinT - Best Known (26−15, 26, s)-Nets in Base 27

Best Known (26−15, 26, s)-Nets in Base 27

Digital (11, 26, 96)-net over F₂₇, using

Digital (11, 26, 114)-net over F₂₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(27²⁶, 114, F₂₇, 15) (dual of [114, 88, 16]-code), using
- 19 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 4 times 0, 1, 13 times 0) [i] based on linear OA(27²³, 92, F₂₇, 15) (dual of [92, 69, 16]-code), using
  - extended algebraic-geometric code AG_e(F,76P) [i] based on function field F/F₂₇ with g(F) = 8 and N(F) ≥ 92, using
    - a curve from the manYPoints database [i]

(11, 26, 150)-net in base 27, using

2 times m-reduction [i] based on (11, 28, 150)-net in base 27, using
- base change [i] based on digital (4, 21, 150)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 149)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 150, using
      - a function field by SÃ©mirat [i]

(11, 26, 154)-net in base 27, using

2 times m-reduction [i] based on (11, 28, 154)-net in base 27, using
- base change [i] based on digital (4, 21, 154)-net over F₈₁, using
  - net from sequence [i] based on digital (4, 153)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 4 and N(F) ≥ 154, using
      - a curve from the manYPoints database [i]

There is no (11, 26, 16822)-net in base 27, because

1 times m-reduction [i] would yield (11, 25, 16822)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 608298 891835 595656 476981 207665 768553 > 27²⁵ [i]