MinT - Best Known (17, 39, s)-Nets in Base 32

Best Known (17, 39, s)-Nets in Base 32

Digital (17, 39, 128)-net over F₃₂, using

Digital (17, 39, 186)-net over F₃₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OA(32³⁹, 186, F₃₂, 22) (dual of [186, 147, 23]-code), using
- 26 step VarÅ¡amovâ€“Edel lengthening with (r_i)Â = (1, 0, 0, 0, 1, 21 times 0) [i] based on linear OA(32³⁷, 158, F₃₂, 22) (dual of [158, 121, 23]-code), using
  - extended algebraic-geometric code AG_e(F,135P) [i] based on function field F/F₃₂ with g(F) = 15 and N(F) ≥ 158, using
    - an algebraic function field by Beelen and Pellikaan [i]

(17, 39, 259)-net in base 32, using

1 times m-reduction [i] based on (17, 40, 259)-net in base 32, using
- base change [i] based on digital (2, 25, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(17, 39, 321)-net in base 32, using

1 times m-reduction [i] based on (17, 40, 321)-net in base 32, using
- base change [i] based on digital (2, 25, 321)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 320)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 2 and N(F) ≥ 321, using
      - sharp bound on the number of rational points on curves with genus 2 [i]

There is no (17, 39, 34358)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 50219 687990 989592 954668 183886 953549 286456 199965 670573 941532 > 32³⁹ [i]