MinT - Best Known (2, 2+46, s)-Nets in Base 27

Best Known (2, 2+46, s)-Nets in Base 27

(2, 2+46, 48)-Net over F₂₇ — Constructive and digital

Digital (2, 48, 48)-net over F₂₇, using

net from sequence [i] based on digital (2, 47)-sequence over F₂₇, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 2 and N(F) ≥ 48, using
  - a function field by GarcÃa and Quoos [i]

(2, 2+46, 204)-Net in Base 27 — Upper bound on s

There is no (2, 48, 205)-net in base 27, because

1 times m-reduction [i] would yield (2, 47, 205)-net in base 27, but
- extracting embedded orthogonal array [i] would yield OA(27⁴⁷, 205, S₂₇, 45), but
  - the linear programming bound shows that MÂ â‰¥ 113487 692928 681005 740327 021988 882047 665664 922335 740996 167610 589817 706401 138356 444308 / 5988 523057 406269 > 27⁴⁷ [i]