MinT - Best Known (25, 25+81, s)-Nets in Base 27

Best Known (25, 25+81, s)-Nets in Base 27

(25, 25+81, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 106, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 106, 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+81, 208)-Net over F₂₇ — Digital

Digital (25, 106, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 106, 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+81, 3447)-Net in Base 27 — Upper bound on s

There is no (25, 106, 3448)-net in base 27, because

1 times m-reduction [i] would yield (25, 105, 3448)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 974751 603947 585078 863665 814780 246356 108134 585509 388939 366927 488375 562787 695595 267735 006522 814793 085151 191212 325129 312357 862178 265769 793338 773936 617729 > 27¹⁰⁵ [i]