MinT - Best Known (16, 16+31, s)-Nets in Base 4

Best Known (16, 16+31, s)-Nets in Base 4

(16, 16+31, 33)-Net over F₄ — Constructive and digital

Digital (16, 47, 33)-net over F₄, using

t-expansion [i] based on digital (15, 47, 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+31, 36)-Net over F₄ — Digital

Digital (16, 47, 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+31, 138)-Net in Base 4 — Upper bound on s

There is no (16, 47, 139)-net in base 4, because

1 times m-reduction [i] would yield (16, 46, 139)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 5122 909558 524300 478829 551360 > 4⁴⁶ [i]