MinT - Best Known (25, 25+77, s)-Nets in Base 27

Best Known (25, 25+77, s)-Nets in Base 27

(25, 25+77, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 102, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 102, 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+77, 208)-Net over F₂₇ — Digital

Digital (25, 102, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 102, 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+77, 3663)-Net in Base 27 — Upper bound on s

There is no (25, 102, 3664)-net in base 27, because

1 times m-reduction [i] would yield (25, 101, 3664)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 3 718201 622142 502776 588050 544812 119774 930289 247796 361983 639370 448794 913354 385158 617658 010846 303720 097231 223574 114740 977207 837437 504282 826359 456737 > 27¹⁰¹ [i]