MinT - Best Known (19, 19+63, s)-Nets in Base 32

Best Known (19, 19+63, s)-Nets in Base 32

(19, 19+63, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 82, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 82, 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]

(19, 19+63, 128)-Net in Base 32 — Constructive

(19, 82, 128)-net in base 32, using

2 times m-reduction [i] based on (19, 84, 128)-net in base 32, using
- base change [i] based on digital (5, 70, 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]

(19, 19+63, 172)-Net over F₃₂ — Digital

Digital (19, 82, 172)-net over F₃₂, using

net from sequence [i] based on digital (19, 171)-sequence over F₃₂, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 19 and N(F) ≥ 172, using
  - a curve from the manYPoints database [i]

(19, 19+63, 3415)-Net in Base 32 — Upper bound on s

There is no (19, 82, 3416)-net in base 32, because

1 times m-reduction [i] would yield (19, 81, 3416)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 83 002854 490484 137676 116650 528217 247779 846046 865016 709580 591198 828123 450488 122362 825645 654715 639875 215813 505441 816285 917160 > 32⁸¹ [i]