Best Known (22−15, 22, s)-Nets in Base 3
(22−15, 22, 16)-Net over F3 — Constructive and digital
Digital (7, 22, 16)-net over F3, using
- net from sequence [i] based on digital (7, 15)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 7 and N(F) ≥ 16, using
(22−15, 22, 27)-Net over F3 — Upper bound on s (digital)
There is no digital (7, 22, 28)-net over F3, because
- extracting embedded orthogonal array [i] would yield linear OA(322, 28, F3, 15) (dual of [28, 6, 16]-code), but
- “HHM†bound on codes from Brouwer’s database [i]
(22−15, 22, 39)-Net in Base 3 — Upper bound on s
There is no (7, 22, 40)-net in base 3, because
- 1 times m-reduction [i] would yield (7, 21, 40)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 11302 336737 > 321 [i]