MinT - Best Known (15−9, 15, s)-Nets in Base 4

Best Known (15−9, 15, s)-Nets in Base 4

(15−9, 15, 18)-Net over F₄ — Constructive and digital

Digital (6, 15, 18)-net over F₄, using

3 times m-reduction [i] based on digital (6, 18, 18)-net over F₄, using
- a shift-net [i]

(15−9, 15, 20)-Net over F₄ — Digital

Digital (6, 15, 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]

(15−9, 15, 91)-Net in Base 4 — Upper bound on s

There is no (6, 15, 92)-net in base 4, because

1 times m-reduction [i] would yield (6, 14, 92)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 272 576014 > 4¹⁴ [i]