MinT - Best Known (66−49, 66, s)-Nets in Base 27

Best Known (66−49, 66, s)-Nets in Base 27

(66−49, 66, 96)-Net over F₂₇ — Constructive and digital

Digital (17, 66, 96)-net over F₂₇, using

t-expansion [i] based on digital (11, 66, 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]

(66−49, 66, 144)-Net over F₂₇ — Digital

Digital (17, 66, 144)-net over F₂₇, using

t-expansion [i] based on digital (16, 66, 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]

(66−49, 66, 2825)-Net in Base 27 — Upper bound on s

There is no (17, 66, 2826)-net in base 27, because

1 times m-reduction [i] would yield (17, 65, 2826)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1097 641606 750950 880179 170817 526096 472078 232027 450834 335132 893573 478625 321436 206307 065125 905521 > 27⁶⁵ [i]