MinT - Best Known (40−30, 40, s)-Nets in Base 4

Best Known (40−30, 40, s)-Nets in Base 4

(40−30, 40, 27)-Net over F₄ — Constructive and digital

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]

(40−30, 40, 56)-Net in Base 4 — Upper bound on s

There is no (10, 40, 57)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁰, 57, S₄, 30), but
- the linear programming bound shows that MÂ â‰¥ 3920 567245 877152 899028 000509 526016 / 2494 923431 > 4⁴⁰ [i]