MinT - Best Known (15, 15+41, s)-Nets in Base 32

Best Known (15, 15+41, s)-Nets in Base 32

(15, 15+41, 120)-Net over F₃₂ — Constructive and digital

Digital (15, 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]

(15, 15+41, 128)-Net in Base 32 — Constructive

(15, 56, 128)-net in base 32, using

4 times m-reduction [i] based on (15, 60, 128)-net in base 32, using
- base change [i] based on digital (5, 50, 128)-net over F₆₄, using
  - net from sequence [i] based on digital (5, 127)-sequence over F₆₄, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 5 and N(F) ≥ 128, using
      - a function field by SÃ©mirat [i]

(15, 15+41, 158)-Net over F₃₂ — Digital

Digital (15, 56, 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+41, 3680)-Net in Base 32 — Upper bound on s

There is no (15, 56, 3681)-net in base 32, because

1 times m-reduction [i] would yield (15, 55, 3681)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 60857 924113 023385 373152 648870 706581 418211 923683 932915 471714 463187 688555 189472 490488 > 32⁵⁵ [i]