Best Known (169−22, 169, s)-Nets in Base 4
(169−22, 169, 95329)-Net over F4 — Constructive and digital
Digital (147, 169, 95329)-net over F4, using
- 41 times duplication [i] based on digital (146, 168, 95329)-net over F4, using
- net defined by OOA [i] based on linear OOA(4168, 95329, F4, 22, 22) (dual of [(95329, 22), 2097070, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4168, 1048619, F4, 22) (dual of [1048619, 1048451, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OA 11-folding and stacking [i] based on linear OA(4168, 1048619, F4, 22) (dual of [1048619, 1048451, 23]-code), using
- net defined by OOA [i] based on linear OOA(4168, 95329, F4, 22, 22) (dual of [(95329, 22), 2097070, 23]-NRT-code), using
(169−22, 169, 517455)-Net over F4 — Digital
Digital (147, 169, 517455)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4169, 517455, F4, 2, 22) (dual of [(517455, 2), 1034741, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4169, 524312, F4, 2, 22) (dual of [(524312, 2), 1048455, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4169, 1048624, F4, 22) (dual of [1048624, 1048455, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4161, 1048576, F4, 22) (dual of [1048576, 1048415, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(4121, 1048576, F4, 17) (dual of [1048576, 1048455, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(48, 48, F4, 4) (dual of [48, 40, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(48, 85, F4, 4) (dual of [85, 77, 5]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- OOA 2-folding [i] based on linear OA(4169, 1048624, F4, 22) (dual of [1048624, 1048455, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(4169, 524312, F4, 2, 22) (dual of [(524312, 2), 1048455, 23]-NRT-code), using
(169−22, 169, large)-Net in Base 4 — Upper bound on s
There is no (147, 169, large)-net in base 4, because
- 20 times m-reduction [i] would yield (147, 149, large)-net in base 4, but