MinT - Best Known (24, 109, s)-Nets in Base 27

Best Known (24, 109, s)-Nets in Base 27

(24, 109, 114)-Net over F₂₇ — Constructive and digital

Digital (24, 109, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 109, 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, 109, 208)-Net over F₂₇ — Digital

Digital (24, 109, 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, 109, 3022)-Net in Base 27 — Upper bound on s

There is no (24, 109, 3023)-net in base 27, because

1 times m-reduction [i] would yield (24, 108, 3023)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 39115 439171 593492 666512 854345 383484 126913 424132 201606 458691 004615 402710 531501 265655 873578 631375 552449 714726 405487 437425 422170 601656 227725 787155 241921 920861 > 27¹⁰⁸ [i]