MinT - Best Known (8, 8+7, s)-Nets in Base 3

Best Known (8, 8+7, s)-Nets in Base 3

(8, 8+7, 34)-Net over F₃ — Constructive and digital

Digital (8, 15, 34)-net over F₃, using

3¹ times duplication [i] based on digital (7, 14, 34)-net over F₃, using
- linear code embedding found in a computer search [i]

(8, 8+7, 150)-Net in Base 3 — Upper bound on s

There is no (8, 15, 151)-net in base 3, because

1 times m-reduction [i] would yield (8, 14, 151)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 4 820827 > 3¹⁴ [i]