MinT - Best Known (22, 56, s)-Nets in Base 32

Best Known (22, 56, s)-Nets in Base 32

(22, 56, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 56, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 56, 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]

(22, 56, 185)-Net over F₃₂ — Digital

Digital (22, 56, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 56, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(22, 56, 258)-Net in Base 32 — Constructive

(22, 56, 258)-net in base 32, using

base change [i] based on digital (1, 35, 258)-net over F₂₅₆, using
- net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
  - Niederreiter sequence [i]

(22, 56, 289)-Net in Base 32

(22, 56, 289)-net in base 32, using

base change [i] based on digital (1, 35, 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]

(22, 56, 21015)-Net in Base 32 — Upper bound on s

There is no (22, 56, 21016)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 1 942824 147570 802966 758265 304631 378182 652399 036724 816244 490435 354032 857786 723388 269197 > 32⁵⁶ [i]