MinT - Best Known (25, 25+75, s)-Nets in Base 27

Best Known (25, 25+75, s)-Nets in Base 27

(25, 25+75, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 100, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 100, 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]

(25, 25+75, 208)-Net over F₂₇ — Digital

Digital (25, 100, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 100, 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]

(25, 25+75, 3789)-Net in Base 27 — Upper bound on s

There is no (25, 100, 3790)-net in base 27, because

1 times m-reduction [i] would yield (25, 99, 3790)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 5093 018285 628974 181004 499489 847561 311081 252823 363763 392800 374532 615543 132435 565572 499539 691829 157883 803595 662724 443235 317111 955724 709075 280069 > 27⁹⁹ [i]