MinT - Best Known (15, 15+26, s)-Nets in Base 32

Best Known (15, 15+26, s)-Nets in Base 32

(15, 15+26, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 41, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 41, 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, 15+26, 158)-Net over F₃₂ — Digital

Digital (15, 41, 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, 15+26, 192)-Net in Base 32 — Constructive

(15, 41, 192)-net in base 32, using

1 times m-reduction [i] based on (15, 42, 192)-net in base 32, using
- base change [i] based on digital (3, 30, 192)-net over F₁₂₈, using
  - net from sequence [i] based on digital (3, 191)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 3 and N(F) ≥ 192, using
      - a function field by SÃ©mirat [i]

(15, 15+26, 10204)-Net in Base 32 — Upper bound on s

There is no (15, 41, 10205)-net in base 32, because

the generalized Rao bound for nets shows that 32^mÂ â‰¥ 51 468396 467949 160272 020877 695813 140716 665964 536324 355774 888624 > 32⁴¹ [i]