MinT - Best Known (16, 38, s)-Nets in Base 32

Best Known (16, 38, s)-Nets in Base 32

(16, 38, 120)-Net over F₃₂ — Constructive and digital

Digital (16, 38, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 38, 120)-net over F₃₂, using
- net from sequence [i] based on digital (11, 119)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 11 and N(F) ≥ 120, using
    - a function field by SÃ©mirat [i]

(16, 38, 158)-Net over F₃₂ — Digital

Digital (16, 38, 158)-net over F₃₂, using

t-expansion [i] based on digital (15, 38, 158)-net over F₃₂, using
- net from sequence [i] based on digital (15, 157)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [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]

(16, 38, 258)-Net in Base 32 — Constructive

(16, 38, 258)-net in base 32, using

2 times m-reduction [i] based on (16, 40, 258)-net in base 32, using
- base change [i] based on digital (1, 25, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(16, 38, 289)-Net in Base 32

(16, 38, 289)-net in base 32, using

2 times m-reduction [i] based on (16, 40, 289)-net in base 32, using
- base change [i] based on digital (1, 25, 289)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 288)-sequence over F₂₅₆, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 1 and N(F) ≥ 289, using
      - sharp bound on the number of rational points on curves with genus 1 [i]

(16, 38, 25070)-Net in Base 32 — Upper bound on s

There is no (16, 38, 25071)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1569 391640 868366 072149 285423 197483 026449 423411 913676 215012 > 32³⁸ [i]