MinT - Best Known (12, 12+16, s)-Nets in Base 27

Best Known (12, 12+16, s)-Nets in Base 27

Digital (12, 28, 96)-net over F₂₇, using

Digital (12, 28, 125)-net over F₂₇, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(27²⁸, 125, F₂₇, 16) (dual of [125, 97, 17]-code), using
- 23 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (2, 5 times 0, 1, 16 times 0) [i] based on linear OA(27²⁵, 99, F₂₇, 16) (dual of [99, 74, 17]-code), using
  - extended algebraic-geometric code AG_e(F,82P) [i] based on function field F/F₂₇ with g(F) = 9 and N(F) ≥ 99, using
    - a curve from the manYPoints database [i]

(12, 28, 160)-net in base 27, using

base change [i] based on digital (5, 21, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(12, 28, 167)-net in base 27, using

base change [i] based on digital (5, 21, 167)-net over F₈₁, using
- net from sequence [i] based on digital (5, 166)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 167, using
    - a curve from the manYPoints database [i]

There is no (12, 28, 14804)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 11972 706219 265745 649288 107726 002667 096001 > 27²⁸ [i]