MinT - Best Known (27, 27+77, s)-Nets in Base 27

Best Known (27, 27+77, s)-Nets in Base 27

(27, 27+77, 114)-Net over F₂₇ — Constructive and digital

Digital (27, 104, 114)-net over F₂₇, using

t-expansion [i] based on digital (23, 104, 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+77, 208)-Net over F₂₇ — Digital

Digital (27, 104, 208)-net over F₂₇, using

t-expansion [i] based on digital (24, 104, 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+77, 4361)-Net in Base 27 — Upper bound on s

There is no (27, 104, 4362)-net in base 27, because

1 times m-reduction [i] would yield (27, 103, 4362)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 2715 165745 309393 816026 912068 593539 702675 826772 100886 817268 104468 987279 087506 640281 657256 734997 408801 726237 085008 036632 296007 343481 772163 540213 430125 > 27¹⁰³ [i]