Best Known (13, 13+7, s)-Nets in Base 3
(13, 13+7, 68)-Net over F3 — Constructive and digital
Digital (13, 20, 68)-net over F3, using
- (u, u+v)-construction [i] based on
(13, 13+7, 81)-Net over F3 — Digital
Digital (13, 20, 81)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(320, 81, F3, 7) (dual of [81, 61, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(320, 121, F3, 7) (dual of [121, 101, 8]-code), using
(13, 13+7, 952)-Net in Base 3 — Upper bound on s
There is no (13, 20, 953)-net in base 3, because
- 1 times m-reduction [i] would yield (13, 19, 953)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1163 126971 > 319 [i]