MinT - Best Known (26, 26+79, s)-Nets in Base 27

Best Known (26, 26+79, s)-Nets in Base 27

(26, 26+79, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 105, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 105, 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]

(26, 26+79, 208)-Net over F₂₇ — Digital

Digital (26, 105, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 105, 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]

(26, 26+79, 3864)-Net in Base 27 — Upper bound on s

There is no (26, 105, 3865)-net in base 27, because

1 times m-reduction [i] would yield (26, 104, 3865)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 72895 541554 005812 808193 740423 509912 707631 605764 676301 564209 851885 103799 410047 738767 419484 932110 188394 459253 579730 235278 375168 362502 120827 465247 265363 > 27¹⁰⁴ [i]