Best Known (128, 128+22, s)-Nets in Base 4
(128, 128+22, 23834)-Net over F4 — Constructive and digital
Digital (128, 150, 23834)-net over F4, using
- net defined by OOA [i] based on linear OOA(4150, 23834, F4, 22, 22) (dual of [(23834, 22), 524198, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4150, 262174, F4, 22) (dual of [262174, 262024, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4150, 262176, F4, 22) (dual of [262176, 262026, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- 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(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(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(21) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4150, 262176, F4, 22) (dual of [262176, 262026, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(4150, 262174, F4, 22) (dual of [262174, 262024, 23]-code), using
(128, 128+22, 129353)-Net over F4 — Digital
Digital (128, 150, 129353)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4150, 129353, F4, 2, 22) (dual of [(129353, 2), 258556, 23]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4150, 131088, F4, 2, 22) (dual of [(131088, 2), 262026, 23]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4150, 262176, F4, 22) (dual of [262176, 262026, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(17) [i] based on
- 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(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(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(21) ⊂ Ce(17) [i] based on
- OOA 2-folding [i] based on linear OA(4150, 262176, F4, 22) (dual of [262176, 262026, 23]-code), using
- discarding factors / shortening the dual code based on linear OOA(4150, 131088, F4, 2, 22) (dual of [(131088, 2), 262026, 23]-NRT-code), using
(128, 128+22, large)-Net in Base 4 — Upper bound on s
There is no (128, 150, large)-net in base 4, because
- 20 times m-reduction [i] would yield (128, 130, large)-net in base 4, but