MinT - Best Known (19−9, 19, s)-Nets in Base 3

Best Known (19−9, 19, s)-Nets in Base 3

(19−9, 19, 26)-Net over F₃ — Constructive and digital

Digital (10, 19, 26)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (2, 6, 14)-net over F₃, using
  - linear code embedding found in a computer search [i]
2. digital (4, 13, 13)-net over F₃, using
  - a shift-net [i]

(19−9, 19, 151)-Net in Base 3 — Upper bound on s

There is no (10, 19, 152)-net in base 3, because

1 times m-reduction [i] would yield (10, 18, 152)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 389 461697 > 3¹⁸ [i]