Best Known (14, 14+6, s)-Nets in Base 3
(14, 14+6, 90)-Net over F3 — Constructive and digital
Digital (14, 20, 90)-net over F3, using
- trace code for nets [i] based on digital (4, 10, 45)-net over F9, using
(14, 14+6, 201)-Net over F3 — Digital
Digital (14, 20, 201)-net over F3, using
- net defined by OOA [i] based on linear OOA(320, 201, F3, 6, 6) (dual of [(201, 6), 1186, 7]-NRT-code), using
- appending kth column [i] based on linear OOA(320, 201, F3, 5, 6) (dual of [(201, 5), 985, 7]-NRT-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(320, 201, F3, 6) (dual of [201, 181, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(320, 242, F3, 6) (dual of [242, 222, 7]-code), using
- the primitive narrow-sense BCH-code C(I) with length 242 = 35−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- discarding factors / shortening the dual code based on linear OA(320, 242, F3, 6) (dual of [242, 222, 7]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(320, 201, F3, 6) (dual of [201, 181, 7]-code), using
- appending kth column [i] based on linear OOA(320, 201, F3, 5, 6) (dual of [(201, 5), 985, 7]-NRT-code), using
(14, 14+6, 1375)-Net in Base 3 — Upper bound on s
There is no (14, 20, 1376)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 3492 667777 > 320 [i]