MinT - Best Known (38−27, 38, s)-Nets in Base 4

Best Known (38−27, 38, s)-Nets in Base 4

(38−27, 38, 27)-Net over F₄ — Constructive and digital

Digital (11, 38, 27)-net over F₄, using

t-expansion [i] based on digital (10, 38, 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]

(38−27, 38, 86)-Net in Base 4 — Upper bound on s

There is no (11, 38, 87)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4³⁸, 87, S₄, 27), but
- the linear programming bound shows that MÂ â‰¥ 750676 473656 767244 506582 044594 315077 520225 769567 027200 / 9 306912 430727 497773 727968 244619 > 4³⁸ [i]