MinT - Best Known (25, 25+47, s)-Nets in Base 27

Best Known (25, 25+47, s)-Nets in Base 27

(25, 25+47, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 72, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 72, 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+47, 172)-Net in Base 27 — Constructive

(25, 72, 172)-net in base 27, using

base change [i] based on digital (7, 54, 172)-net over F₈₁, using
- net from sequence [i] based on digital (7, 171)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 7 and N(F) ≥ 172, using
    - a function field by SÃ©mirat [i]

(25, 25+47, 208)-Net over F₂₇ — Digital

Digital (25, 72, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 72, 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+47, 9495)-Net in Base 27 — Upper bound on s

There is no (25, 72, 9496)-net in base 27, because

1 times m-reduction [i] would yield (25, 71, 9496)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 424442 426609 524936 082004 672288 381628 113910 786723 443283 733677 972659 952117 239672 174088 350951 428955 992673 > 27⁷¹ [i]