MinT - Best Known (69−53, 69, s)-Nets in Base 27

Best Known (69−53, 69, s)-Nets in Base 27

(69−53, 69, 96)-Net over F₂₇ — Constructive and digital

Digital (16, 69, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 69, 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]

(69−53, 69, 144)-Net over F₂₇ — Digital

Digital (16, 69, 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]

(69−53, 69, 2234)-Net in Base 27 — Upper bound on s

There is no (16, 69, 2235)-net in base 27, because

1 times m-reduction [i] would yield (16, 68, 2235)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 21 518476 120442 898645 767336 702068 736627 197421 338232 727807 570896 829743 348686 024467 870855 876410 499381 > 27⁶⁸ [i]