MinT - Best Known (28, 28+82, s)-Nets in Base 27

Best Known (28, 28+82, s)-Nets in Base 27

(28, 28+82, 114)-Net over F₂₇ — Constructive and digital

Digital (28, 110, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 110, 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]

(28, 28+82, 208)-Net over F₂₇ — Digital

Digital (28, 110, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 110, 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]

(28, 28+82, 4275)-Net in Base 27 — Upper bound on s

There is no (28, 110, 4276)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 28 284558 078370 088378 768909 454403 040018 763570 401654 304581 746336 317315 479026 053166 853348 566936 975292 473219 934353 545687 200184 536080 826613 179284 147700 639683 151433 > 27¹¹⁰ [i]