MinT - Best Known (22, 22+79, s)-Nets in Base 32

Best Known (22, 22+79, s)-Nets in Base 32

(22, 22+79, 120)-Net over F₃₂ — Constructive and digital

Digital (22, 101, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 101, 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]

(22, 22+79, 128)-Net in Base 32 — Constructive

(22, 101, 128)-net in base 32, using

1 times m-reduction [i] based on (22, 102, 128)-net in base 32, using
- base change [i] based on digital (5, 85, 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]

(22, 22+79, 185)-Net over F₃₂ — Digital

Digital (22, 101, 185)-net over F₃₂, using

t-expansion [i] based on digital (21, 101, 185)-net over F₃₂, using
- net from sequence [i] based on digital (21, 184)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 21 and N(F) ≥ 185, using
    - a curve from the manYPoints database [i]

(22, 22+79, 3572)-Net in Base 32 — Upper bound on s

There is no (22, 101, 3573)-net in base 32, because

1 times m-reduction [i] would yield (22, 100, 3573)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 3 291952 794417 073486 152394 157658 100047 775510 013322 502953 121779 391203 475821 142583 957857 014776 904614 311297 815376 136588 949703 163655 654080 518617 913551 666736 > 32¹⁰⁰ [i]