MinT - Best Known (32−19, 32, s)-Nets in Base 32

Best Known (32−19, 32, s)-Nets in Base 32

(32−19, 32, 120)-Net over F₃₂ — Constructive and digital

Digital (13, 32, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 32, 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]

(32−19, 32, 129)-Net over F₃₂ — Digital

Digital (13, 32, 129)-net over F₃₂, using

t-expansion [i] based on digital (12, 32, 129)-net over F₃₂, using
- net from sequence [i] based on digital (12, 128)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 12 and N(F) ≥ 129, using
    - a curve from the manYPoints database [i]

(32−19, 32, 258)-Net in Base 32 — Constructive

(13, 32, 258)-net in base 32, using

base change [i] based on digital (1, 20, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(32−19, 32, 289)-Net in Base 32

(13, 32, 289)-net in base 32, using

base change [i] based on digital (1, 20, 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]

(32−19, 32, 20450)-Net in Base 32 — Upper bound on s

There is no (13, 32, 20451)-net in base 32, because

1 times m-reduction [i] would yield (13, 31, 20451)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 45681 778091 463190 268104 322532 692834 825508 870072 > 32³¹ [i]