Best Known (14−5, 14, s)-Nets in Base 3
(14−5, 14, 103)-Net over F3 — Constructive and digital
Digital (9, 14, 103)-net over F3, using
- 31 times duplication [i] based on digital (8, 13, 103)-net over F3, using
(14−5, 14, 104)-Net over F3 — Digital
Digital (9, 14, 104)-net over F3, using
- net defined by OOA [i] based on linear OOA(314, 104, F3, 5, 5) (dual of [(104, 5), 506, 6]-NRT-code), using
- appending kth column [i] based on linear OOA(314, 104, F3, 4, 5) (dual of [(104, 4), 402, 6]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(314, 104, F3, 5) (dual of [104, 90, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(314, 146, F3, 5) (dual of [146, 132, 6]-code), using
- trace code [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(314, 146, F3, 5) (dual of [146, 132, 6]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(314, 104, F3, 5) (dual of [104, 90, 6]-code), using
- appending kth column [i] based on linear OOA(314, 104, F3, 4, 5) (dual of [(104, 4), 402, 6]-NRT-code), using
(14−5, 14, 891)-Net in Base 3 — Upper bound on s
There is no (9, 14, 892)-net in base 3, because
- 1 times m-reduction [i] would yield (9, 13, 892)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 596681 > 313 [i]