MinT - Best Known (97−71, 97, s)-Nets in Base 27

Best Known (97−71, 97, s)-Nets in Base 27

(97−71, 97, 114)-Net over F₂₇ — Constructive and digital

Digital (26, 97, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 97, 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]

(97−71, 97, 208)-Net over F₂₇ — Digital

Digital (26, 97, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 97, 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]

(97−71, 97, 4493)-Net in Base 27 — Upper bound on s

There is no (26, 97, 4494)-net in base 27, because

1 times m-reduction [i] would yield (26, 96, 4494)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 259336 142470 244325 594853 438300 972853 882759 574139 732830 146543 934144 330501 090720 040486 733853 565881 772055 272490 158954 823374 822165 226179 496529 > 27⁹⁶ [i]