MinT - Best Known (29, 29+81, s)-Nets in Base 27

Best Known (29, 29+81, s)-Nets in Base 27

(29, 29+81, 114)-Net over F₂₇ — Constructive and digital

Digital (29, 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]

(29, 29+81, 208)-Net over F₂₇ — Digital

Digital (29, 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]

(29, 29+81, 4801)-Net in Base 27 — Upper bound on s

There is no (29, 110, 4802)-net in base 27, because

1 times m-reduction [i] would yield (29, 109, 4802)-net in base 27, but
- the generalized Rao bound for nets shows that 27^mÂ â‰¥ 1 047236 822341 526684 148548 249563 312847 646717 665455 136169 809035 125068 104179 105341 256957 250090 041786 750404 254938 740440 469543 131240 938828 996173 967321 332168 583057 > 27¹⁰⁹ [i]