MinT - Best Known (27, 27+78, s)-Nets in Base 27

Best Known (27, 27+78, s)-Nets in Base 27

(27, 27+78, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 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]

(27, 27+78, 208)-Net over F₂₇ — Digital

Digital (27, 105, 208)-net over F₂₇, using

t-expansion [i] based on 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]

(27, 27+78, 4207)-Net in Base 27 — Upper bound on s

There is no (27, 105, 4208)-net in base 27, because

the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 974943 216705 478748 430812 429988 704883 065063 907378 089596 836025 543909 365220 841677 792689 183298 957133 646738 688012 090056 003535 626607 043445 071641 773260 243905 > 27¹⁰⁵ [i]