MinT - Best Known (29, 29+67, s)-Nets in Base 27

Best Known (29, 29+67, s)-Nets in Base 27

(29, 29+67, 114)-Net over F₂₇ — Constructive and digital

Digital (29, 96, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 96, 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]

(29, 29+67, 160)-Net in Base 27 — Constructive

(29, 96, 160)-net in base 27, using

base change [i] based on digital (5, 72, 160)-net over F₈₁, using
- net from sequence [i] based on digital (5, 159)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 5 and N(F) ≥ 160, using
    - a function field by SÃ©mirat [i]

(29, 29+67, 208)-Net over F₂₇ — Digital

Digital (29, 96, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 96, 208)-net over F₂₇, using
- net from sequence [i] based on digital (24, 207)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 24 and N(F) ≥ 208, using
    - an algebraic function field by Beelen and Pellikaan [i]

(29, 29+67, 6665)-Net in Base 27 — Upper bound on s

There is no (29, 96, 6666)-net in base 27, because

1 times m-reduction [i] would yield (29, 95, 6666)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 9551 004873 456958 389599 492431 649694 026929 404607 597845 266316 505687 915260 062327 551427 464690 365914 406638 969528 109926 585488 952559 395149 827525 > 27⁹⁵ [i]