MinT - Best Known (108−83, 108, s)-Nets in Base 27

Best Known (108−83, 108, s)-Nets in Base 27

(108−83, 108, 114)-Net over F₂₇ — Constructive and digital

Digital (25, 108, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 108, 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]

(108−83, 108, 208)-Net over F₂₇ — Digital

Digital (25, 108, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 108, 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]

(108−83, 108, 3354)-Net in Base 27 — Upper bound on s

There is no (25, 108, 3355)-net in base 27, because

1 times m-reduction [i] would yield (25, 107, 3355)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1435 028892 274557 624384 422094 504318 965113 515872 740161 701182 507914 653967 600642 082404 562848 376210 705574 099270 148994 216260 964447 180026 289223 736652 182089 191023 > 27¹⁰⁷ [i]