MinT - Best Known (26, 26+35, s)-Nets in Base 32

Best Known (26, 26+35, s)-Nets in Base 32

Digital (26, 61, 142)-net over F₃₂, using

Digital (26, 61, 226)-net over F₃₂, using

embedding of OOA with Gilbertâ€“VarÅ¡amov bound [i] based on linear OOA(32⁶¹, 226, F₃₂, 2, 35) (dual of [(226, 2), 391, 36]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(32⁵⁹, 225, F₃₂, 2, 35) (dual of [(225, 2), 391, 36]-NRT-code), using
  - extended algebraic-geometric NRT-code AG_e(2;F,414P) [i] based on function field F/F₃₂ with g(F) = 24 and N(F) ≥ 225, using
    - a curve from the manYPoints database [i]

(26, 61, 259)-net in base 32, using

3 times m-reduction [i] based on (26, 64, 259)-net in base 32, using
- base change [i] based on digital (2, 40, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(26, 61, 321)-net in base 32, using

3 times m-reduction [i] based on (26, 64, 321)-net in base 32, using
- base change [i] based on digital (2, 40, 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 (26, 61, 47512)-net in base 32, because

1 times m-reduction [i] would yield (26, 60, 47512)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 2 037345 901205 794730 339088 525194 691361 016200 018319 313844 665058 920499 999430 396222 998432 297429 > 32⁶⁰ [i]