MinT - Best Known (6, 6+15, s)-Nets in Base 4

Best Known (6, 6+15, s)-Nets in Base 4

(6, 6+15, 17)-Net over F₄ — Constructive and digital

Digital (6, 21, 17)-net over F₄, using

t-expansion [i] based on digital (5, 21, 17)-net over F₄, using
- net from sequence [i] based on digital (5, 16)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]

(6, 6+15, 20)-Net over F₄ — Digital

Digital (6, 21, 20)-net over F₄, using

net from sequence [i] based on digital (6, 19)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 6 and N(F) ≥ 20, using
  - Drinfeld modules of rank 1 [i]

(6, 6+15, 54)-Net in Base 4 — Upper bound on s

There is no (6, 21, 55)-net in base 4, because

1 times m-reduction [i] would yield (6, 20, 55)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 1 236378 409564 > 4²⁰ [i]