MinT - Best Known (24, 24+75, s)-Nets in Base 27

Best Known (24, 24+75, s)-Nets in Base 27

(24, 24+75, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 99, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 99, 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]

(24, 24+75, 208)-Net over F₂₇ — Digital

Digital (24, 99, 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]

(24, 24+75, 3464)-Net in Base 27 — Upper bound on s

There is no (24, 99, 3465)-net in base 27, because

1 times m-reduction [i] would yield (24, 98, 3465)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 187 935615 946998 096622 118642 880440 642650 299935 799197 808515 052886 378250 432951 514274 159073 784601 867734 051483 468636 673987 790800 359059 207602 433595 > 27⁹⁸ [i]