Best Known (126−18, 126, s)-Nets in Base 4
(126−18, 126, 29132)-Net over F4 — Constructive and digital
Digital (108, 126, 29132)-net over F4, using
- net defined by OOA [i] based on linear OOA(4126, 29132, F4, 18, 18) (dual of [(29132, 18), 524250, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(4126, 262188, F4, 18) (dual of [262188, 262062, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4125, 262187, F4, 18) (dual of [262187, 262062, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4118, 262144, F4, 18) (dual of [262144, 262026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4125, 262187, F4, 18) (dual of [262187, 262062, 19]-code), using
- OA 9-folding and stacking [i] based on linear OA(4126, 262188, F4, 18) (dual of [262188, 262062, 19]-code), using
(126−18, 126, 131094)-Net over F4 — Digital
Digital (108, 126, 131094)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4126, 131094, F4, 2, 18) (dual of [(131094, 2), 262062, 19]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4126, 262188, F4, 18) (dual of [262188, 262062, 19]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4125, 262187, F4, 18) (dual of [262187, 262062, 19]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- linear OA(4118, 262144, F4, 18) (dual of [262144, 262026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(482, 262144, F4, 13) (dual of [262144, 262062, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(17) ⊂ Ce(12) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4125, 262187, F4, 18) (dual of [262187, 262062, 19]-code), using
- OOA 2-folding [i] based on linear OA(4126, 262188, F4, 18) (dual of [262188, 262062, 19]-code), using
(126−18, 126, large)-Net in Base 4 — Upper bound on s
There is no (108, 126, large)-net in base 4, because
- 16 times m-reduction [i] would yield (108, 110, large)-net in base 4, but