MinT - Best Known (105−89, 105, s)-Nets in Base 27

Best Known (105−89, 105, s)-Nets in Base 27

(105−89, 105, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 105, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 105, 96)-net over F₂₇, using
- net from sequence [i] based on digital (11, 95)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 11 and N(F) ≥ 96, using
    - an explicitly constructive algebraic function field [i]

(105−89, 105, 144)-Net over F₂₇ — Digital

Digital (16, 105, 144)-net over F₂₇, using

net from sequence [i] based on digital (16, 143)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 16 and N(F) ≥ 144, using
  - a curve from the manYPoints database [i]

(105−89, 105, 1580)-Net in Base 27 — Upper bound on s

There is no (16, 105, 1581)-net in base 27, because

1 times m-reduction [i] would yield (16, 104, 1581)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 73220 747887 435636 606799 751654 784763 188187 197920 523672 151143 003401 421532 786258 082685 630735 169180 247065 811913 617281 134994 089265 615225 004041 738022 996945 > 27¹⁰⁴ [i]