Best Known (2, 2+4, s)-Nets in Base 3
(2, 2+4, 14)-Net over F3 — Constructive and digital
Digital (2, 6, 14)-net over F3, using
(2, 2+4, 14)-Net over F3 — Upper bound on s (digital)
There is no digital (2, 6, 15)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(36, 15, F3, 4) (dual of [15, 9, 5]-code), but
- “vE2†bound on codes from Brouwer’s database [i]
(2, 2+4, 17)-Net in Base 3 — Upper bound on s
There is no (2, 6, 18)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 757 > 36 [i]