Best Known (130−25, 130, s)-Nets in Base 5
(130−25, 130, 1305)-Net over F5 — Constructive and digital
Digital (105, 130, 1305)-net over F5, using
- net defined by OOA [i] based on linear OOA(5130, 1305, F5, 25, 25) (dual of [(1305, 25), 32495, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5130, 15661, F5, 25) (dual of [15661, 15531, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(5130, 15664, F5, 25) (dual of [15664, 15534, 26]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(5130, 15664, F5, 25) (dual of [15664, 15534, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5130, 15661, F5, 25) (dual of [15661, 15531, 26]-code), using
(130−25, 130, 15664)-Net over F5 — Digital
Digital (105, 130, 15664)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5130, 15664, F5, 25) (dual of [15664, 15534, 26]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(59, 39, F5, 5) (dual of [39, 30, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
(130−25, 130, large)-Net in Base 5 — Upper bound on s
There is no (105, 130, large)-net in base 5, because
- 23 times m-reduction [i] would yield (105, 107, large)-net in base 5, but