MinT - Best Known (23, 23+87, s)-Nets in Base 27

Best Known (23, 23+87, s)-Nets in Base 27

(23, 23+87, 114)-Net over F₂₇ — Constructive and digital

Digital (23, 110, 114)-net over F₂₇, using

net from sequence [i] based on digital (23, 113)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 23 and N(F) ≥ 114, using
  - an explicitly constructive algebraic function field [i]

(23, 23+87, 163)-Net over F₂₇ — Digital

Digital (23, 110, 163)-net over F₂₇, using

t-expansion [i] based on digital (21, 110, 163)-net over F₂₇, using
- net from sequence [i] based on digital (21, 162)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 21 and N(F) ≥ 163, using
    - a curve from the manYPoints database [i]

(23, 23+87, 2736)-Net in Base 27 — Upper bound on s

There is no (23, 110, 2737)-net in base 27, because

1 times m-reduction [i] would yield (23, 109, 2737)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 045150 281425 150418 819638 083815 950029 866638 971763 964518 231790 866137 330167 497602 498250 500276 794620 606286 439259 918616 519512 897781 658987 453145 625525 692844 372675 > 27¹⁰⁹ [i]