Best Known (12, 18, s)-Nets in Base 5
(12, 18, 210)-Net over F5 — Constructive and digital
Digital (12, 18, 210)-net over F5, using
- net defined by OOA [i] based on linear OOA(518, 210, F5, 6, 6) (dual of [(210, 6), 1242, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(518, 630, F5, 6) (dual of [630, 612, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(517, 625, F5, 6) (dual of [625, 608, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(513, 625, F5, 4) (dual of [625, 612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- OA 3-folding and stacking [i] based on linear OA(518, 630, F5, 6) (dual of [630, 612, 7]-code), using
(12, 18, 515)-Net over F5 — Digital
Digital (12, 18, 515)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(518, 515, F5, 6) (dual of [515, 497, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(518, 630, F5, 6) (dual of [630, 612, 7]-code), using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- linear OA(517, 625, F5, 6) (dual of [625, 608, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(513, 625, F5, 4) (dual of [625, 612, 5]-code), using an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 624 = 54−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- linear OA(51, 5, F5, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(51, s, F5, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(5) ⊂ Ce(3) [i] based on
- discarding factors / shortening the dual code based on linear OA(518, 630, F5, 6) (dual of [630, 612, 7]-code), using
(12, 18, 7096)-Net in Base 5 — Upper bound on s
There is no (12, 18, 7097)-net in base 5, because
- the generalized Rao bound for nets shows that 5m ≥ 3 815700 999645 > 518 [i]