MinT - Best Known (15, 37, s)-Nets in Base 32

Best Known (15, 37, s)-Nets in Base 32

(15, 37, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 37, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 37, 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]

(15, 37, 158)-Net over F₃₂ — Digital

Digital (15, 37, 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]

(15, 37, 257)-Net in Base 32 — Constructive

(15, 37, 257)-net in base 32, using

3 times m-reduction [i] based on (15, 40, 257)-net in base 32, using
- base change [i] based on digital (0, 25, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]

(15, 37, 18293)-Net in Base 32 — Upper bound on s

There is no (15, 37, 18294)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 49 047444 061210 083265 135273 277604 732004 983070 267999 841580 > 32³⁷ [i]