Best Known (143, 168, s)-Nets in Base 4
(143, 168, 21847)-Net over F4 — Constructive and digital
Digital (143, 168, 21847)-net over F4, using
- 42 times duplication [i] based on digital (141, 166, 21847)-net over F4, using
- net defined by OOA [i] based on linear OOA(4166, 21847, F4, 25, 25) (dual of [(21847, 25), 546009, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4166, 262165, F4, 25) (dual of [262165, 261999, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4145, 262144, F4, 22) (dual of [262144, 261999, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(43, 21, F4, 2) (dual of [21, 18, 3]-code), using
- Hamming code H(3,4) [i]
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(4166, 262165, F4, 25) (dual of [262165, 261999, 26]-code), using
- net defined by OOA [i] based on linear OOA(4166, 21847, F4, 25, 25) (dual of [(21847, 25), 546009, 26]-NRT-code), using
(143, 168, 105312)-Net over F4 — Digital
Digital (143, 168, 105312)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4168, 105312, F4, 2, 25) (dual of [(105312, 2), 210456, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4168, 131088, F4, 2, 25) (dual of [(131088, 2), 262008, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4168, 262176, F4, 25) (dual of [262176, 262008, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- linear OA(4163, 262144, F4, 25) (dual of [262144, 261981, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4136, 262144, F4, 21) (dual of [262144, 262008, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-cap in PG(4,4)), using
- discarding factors / shortening the dual code based on linear OA(45, 41, F4, 3) (dual of [41, 36, 4]-code or 41-cap in PG(4,4)), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- OOA 2-folding [i] based on linear OA(4168, 262176, F4, 25) (dual of [262176, 262008, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(4168, 131088, F4, 2, 25) (dual of [(131088, 2), 262008, 26]-NRT-code), using
(143, 168, large)-Net in Base 4 — Upper bound on s
There is no (143, 168, large)-net in base 4, because
- 23 times m-reduction [i] would yield (143, 145, large)-net in base 4, but