MinT - Best Known (25, 25+70, s)-Nets in Base 27

Best Known (25, 25+70, s)-Nets in Base 27

(25, 25+70, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 95, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 95, 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+70, 208)-Net over F₂₇ — Digital

Digital (25, 95, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 95, 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+70, 4087)-Net in Base 27 — Upper bound on s

There is no (25, 95, 4088)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 9565 587967 490877 958365 444751 174737 098215 773062 310113 235933 539231 457858 028605 182223 460619 846963 603803 006979 754502 990692 714743 431884 880545 > 27⁹⁵ [i]