Best Known (9, 15, s)-Nets in Base 3
(9, 15, 42)-Net over F3 — Constructive and digital
Digital (9, 15, 42)-net over F3, using
- 32 times duplication [i] based on digital (7, 13, 42)-net over F3, using
(9, 15, 49)-Net over F3 — Digital
Digital (9, 15, 49)-net over F3, using
- net defined by OOA [i] based on linear OOA(315, 49, F3, 6, 6) (dual of [(49, 6), 279, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(315, 49, F3, 5, 6) (dual of [(49, 5), 230, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(315, 49, F3, 6) (dual of [49, 34, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(315, 85, F3, 6) (dual of [85, 70, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(315, 49, F3, 6) (dual of [49, 34, 7]-code), using
- appending kth column [i] based on linear OOA(315, 49, F3, 5, 6) (dual of [(49, 5), 230, 7]-NRT-code), using
(9, 15, 218)-Net in Base 3 — Upper bound on s
There is no (9, 15, 219)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 14 487435 > 315 [i]