MinT - Best Known (91−67, 91, s)-Nets in Base 27

Best Known (91−67, 91, s)-Nets in Base 27

(91−67, 91, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 91, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 91, 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]

(91−67, 91, 208)-Net over F₂₇ — Digital

Digital (24, 91, 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]

(91−67, 91, 4038)-Net in Base 27 — Upper bound on s

There is no (24, 91, 4039)-net in base 27, because

1 times m-reduction [i] would yield (24, 90, 4039)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 666 132314 918730 072495 433408 765657 852310 018277 822360 744362 594199 183326 238304 676268 625971 153010 279689 067897 212497 803289 441608 887031 > 27⁹⁰ [i]