MinT - Best Known (24, 24+81, s)-Nets in Base 27

Best Known (24, 24+81, s)-Nets in Base 27

(24, 24+81, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 105, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 105, 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+81, 208)-Net over F₂₇ — Digital

Digital (24, 105, 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+81, 3173)-Net in Base 27 — Upper bound on s

There is no (24, 105, 3174)-net in base 27, because

1 times m-reduction [i] would yield (24, 104, 3174)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 73479 518233 916980 492910 648604 674620 805694 600021 295539 462952 270502 807358 728149 772167 003244 972652 982703 269298 464127 363308 029219 573612 905736 641693 729553 > 27¹⁰⁴ [i]