MinT - Best Known (19, 19+61, s)-Nets in Base 32

Best Known (19, 19+61, s)-Nets in Base 32

(19, 19+61, 120)-Net over F₃₂ — Constructive and digital

Digital (19, 80, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 80, 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+61, 128)-Net in Base 32 — Constructive

(19, 80, 128)-net in base 32, using

4 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+61, 172)-Net over F₃₂ — Digital

Digital (19, 80, 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+61, 3557)-Net in Base 32 — Upper bound on s

There is no (19, 80, 3558)-net in base 32, because

1 times m-reduction [i] would yield (19, 79, 3558)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 81251 944699 822053 767146 635297 874965 464130 760033 962901 470622 757475 303519 365716 308262 527533 356597 781212 208651 215157 994512 > 32⁷⁹ [i]