MinT - Best Known (11, 11+14, s)-Nets in Base 32

Best Known (11, 11+14, s)-Nets in Base 32

(11, 11+14, 120)-Net over F₃₂ — Constructive and digital

Digital (11, 25, 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]

(11, 11+14, 150)-Net over F₃₂ — Digital

Digital (11, 25, 150)-net over F₃₂, using

Gilbertâ€“VarÅ¡amov bound [i]

(11, 11+14, 258)-Net in Base 32 — Constructive

(11, 25, 258)-net in base 32, using

32¹ times duplication [i] based on (10, 24, 258)-net in base 32, using
- base change [i] based on digital (1, 15, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(11, 11+14, 289)-Net in Base 32

(11, 25, 289)-net in base 32, using

32¹ times duplication [i] based on (10, 24, 289)-net in base 32, using
- base change [i] based on digital (1, 15, 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]

(11, 11+14, 25884)-Net in Base 32 — Upper bound on s

There is no (11, 25, 25885)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 42 541943 287809 145623 942988 331964 590168 > 32²⁵ [i]