MinT - Best Known (16, 16+33, s)-Nets in Base 4

Best Known (16, 16+33, s)-Nets in Base 4

(16, 16+33, 33)-Net over F₄ — Constructive and digital

Digital (16, 49, 33)-net over F₄, using

t-expansion [i] based on digital (15, 49, 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]

(16, 16+33, 36)-Net over F₄ — Digital

Digital (16, 49, 36)-net over F₄, using

net from sequence [i] based on digital (16, 35)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 16 and N(F) ≥ 36, using
  - Drinfeld modules of rank 1 [i]

(16, 16+33, 131)-Net in Base 4 — Upper bound on s

There is no (16, 49, 132)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁴⁹, 132, S₄, 33), but
- the linear programming bound shows that MÂ â‰¥ 15 114989 228406 347488 033746 516185 463747 303837 999665 881936 924009 037824 000000 / 45 404812 302889 192810 925950 053918 027049 414939 > 4⁴⁹ [i]