MinT - Best Known (22−13, 22, s)-Nets in Base 4

Best Known (22−13, 22, s)-Nets in Base 4

(22−13, 22, 23)-Net over F₄ — Constructive and digital

Digital (9, 22, 23)-net over F₄, using

1 times m-reduction [i] based on digital (9, 23, 23)-net over F₄, using
- a shift-net [i]

(22−13, 22, 26)-Net over F₄ — Digital

Digital (9, 22, 26)-net over F₄, using

net from sequence [i] based on digital (9, 25)-sequence over F₄, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 9 and N(F) ≥ 26, using
  - Drinfeld modules of rank 1 [i]

(22−13, 22, 123)-Net in Base 4 — Upper bound on s

There is no (9, 22, 124)-net in base 4, because

1 times m-reduction [i] would yield (9, 21, 124)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 4 545152 669458 > 4²¹ [i]