MinT - Best Known (40−29, 40, s)-Nets in Base 4

Best Known (40−29, 40, s)-Nets in Base 4

(40−29, 40, 27)-Net over F₄ — Constructive and digital

Digital (11, 40, 27)-net over F₄, using

t-expansion [i] based on digital (10, 40, 27)-net over F₄, using
- net from sequence [i] based on digital (10, 26)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 10 and N(F) ≥ 27, using
    - an explicitly constructive algebraic function field [i]

(40−29, 40, 76)-Net in Base 4 — Upper bound on s

There is no (11, 40, 77)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁰, 77, S₄, 29), but
- the linear programming bound shows that MÂ â‰¥ 4251 685109 878307 148388 698599 073401 771124 147462 202708 468242 965476 282402 508945 965409 202205 622272 / 3490 809154 964403 279262 795000 811904 506085 532515 137607 243270 620618 690625 > 4⁴⁰ [i]