Best Known (141−26, 141, s)-Nets in Base 4
(141−26, 141, 1263)-Net over F4 — Constructive and digital
Digital (115, 141, 1263)-net over F4, using
- net defined by OOA [i] based on linear OOA(4141, 1263, F4, 26, 26) (dual of [(1263, 26), 32697, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4141, 16419, F4, 26) (dual of [16419, 16278, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- OA 13-folding and stacking [i] based on linear OA(4141, 16419, F4, 26) (dual of [16419, 16278, 27]-code), using
(141−26, 141, 10604)-Net over F4 — Digital
Digital (115, 141, 10604)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4141, 10604, F4, 26) (dual of [10604, 10463, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4141, 16419, F4, 26) (dual of [16419, 16278, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- linear OA(4134, 16384, F4, 26) (dual of [16384, 16250, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4106, 16384, F4, 21) (dual of [16384, 16278, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(47, 35, F4, 4) (dual of [35, 28, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(25) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(4141, 16419, F4, 26) (dual of [16419, 16278, 27]-code), using
(141−26, 141, 6402056)-Net in Base 4 — Upper bound on s
There is no (115, 141, 6402057)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 7 770681 029251 972561 072549 162904 068912 655927 502291 363928 488608 867379 015597 053042 375680 > 4141 [i]