MinT - Best Known (16, 16+45, s)-Nets in Base 4

Best Known (16, 16+45, s)-Nets in Base 4

(16, 16+45, 33)-Net over F₄ — Constructive and digital

Digital (16, 61, 33)-net over F₄, using

t-expansion [i] based on digital (15, 61, 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+45, 36)-Net over F₄ — Digital

Digital (16, 61, 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+45, 76)-Net in Base 4 — Upper bound on s

There is no (16, 61, 77)-net in base 4, because

extracting embedded orthogonal array [i] would yield OA(4⁶¹, 77, S₄, 45), but
- the linear programming bound shows that MÂ â‰¥ 87771 116150 262149 392012 316054 470316 656445 882368 / 16226 709967 > 4⁶¹ [i]