MinT - Best Known (94−61, 94, s)-Nets in Base 32

Best Known (94−61, 94, s)-Nets in Base 32

(94−61, 94, 120)-Net over F₃₂ — Constructive and digital

Digital (33, 94, 120)-net over F₃₂, using

t-expansion [i] based on digital (11, 94, 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]

(94−61, 94, 216)-Net in Base 32 — Constructive

(33, 94, 216)-net in base 32, using

4 times m-reduction [i] based on (33, 98, 216)-net in base 32, using
- base change [i] based on digital (5, 70, 216)-net over F₁₂₈, using
  - net from sequence [i] based on digital (5, 215)-sequence over F₁₂₈, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₂₈ with g(F) = 5 and N(F) ≥ 216, using
      - a function field by SÃ©mirat [i]

(94−61, 94, 273)-Net over F₃₂ — Digital

Digital (33, 94, 273)-net over F₃₂, using

t-expansion [i] based on digital (30, 94, 273)-net over F₃₂, using
- net from sequence [i] based on digital (30, 272)-sequence over F₃₂, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃₂ with g(F) = 30 and N(F) ≥ 273, using
    - a curve from the manYPoints database [i]

(94−61, 94, 17989)-Net in Base 32 — Upper bound on s

There is no (33, 94, 17990)-net in base 32, because

1 times m-reduction [i] would yield (33, 93, 17990)-net in base 32, but
- the generalized Rao bound for nets shows that 32^mÂ â‰¥ 95 350041 989280 967580 151770 212862 455046 091503 974031 465868 224415 572769 543688 263577 942237 019202 791619 070985 606590 547521 353728 705061 610684 791584 > 32⁹³ [i]