MinT - Best Known (48−33, 48, s)-Nets in Base 4

Best Known (48−33, 48, s)-Nets in Base 4

(48−33, 48, 33)-Net over F₄ — Constructive and digital

Digital (15, 48, 33)-net over F₄, using

net from sequence [i] based on digital (15, 32)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 33, using
  - an explicitly constructive algebraic function field [i]

(48−33, 48, 35)-Net over F₄ — Digital

Digital (15, 48, 35)-net over F₄, using

net from sequence [i] based on digital (15, 34)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 15 and N(F) ≥ 35, using
  - a curve from the manYPoints database [i]

(48−33, 48, 117)-Net in Base 4 — Upper bound on s

There is no (15, 48, 118)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁸, 118, S₄, 33), but
- the linear programming bound shows that MÂ â‰¥ 11741 391231 673162 520784 823169 575929 136281 422846 471752 288804 624247 186167 273881 600000 / 141904 351037 772816 847773 975434 784371 947508 137187 747933 > 4⁴⁸ [i]