MinT - Best Known (27, 27+61, s)-Nets in Base 27

Best Known (27, 27+61, s)-Nets in Base 27

(27, 27+61, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 88, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 88, 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]

(27, 27+61, 160)-Net in Base 27 — Constructive

(27, 88, 160)-net in base 27, using

base change [i] based on digital (5, 66, 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]

(27, 27+61, 208)-Net over F₂₇ — Digital

Digital (27, 88, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 88, 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]

(27, 27+61, 6542)-Net in Base 27 — Upper bound on s

There is no (27, 88, 6543)-net in base 27, because

1 times m-reduction [i] would yield (27, 87, 6543)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 33881 690523 400071 675608 213594 542933 909714 701327 001840 198081 811285 734755 003377 120929 604768 842257 886541 555892 814758 725973 514645 > 27⁸⁷ [i]