Best Known (101, 123, s)-Nets in Base 4
(101, 123, 1492)-Net over F4 — Constructive and digital
Digital (101, 123, 1492)-net over F4, using
- 44 times duplication [i] based on digital (97, 119, 1492)-net over F4, using
- net defined by OOA [i] based on linear OOA(4119, 1492, F4, 22, 22) (dual of [(1492, 22), 32705, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(4119, 16412, F4, 22) (dual of [16412, 16293, 23]-code), using
- construction XX applied to Ce(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(492, 16384, F4, 18) (dual of [16384, 16292, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(45, 27, F4, 3) (dual of [27, 22, 4]-code or 27-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
- linear OA(40, 1, F4, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(21) ⊂ Ce(17) ⊂ Ce(16) [i] based on
- OA 11-folding and stacking [i] based on linear OA(4119, 16412, F4, 22) (dual of [16412, 16293, 23]-code), using
- net defined by OOA [i] based on linear OOA(4119, 1492, F4, 22, 22) (dual of [(1492, 22), 32705, 23]-NRT-code), using
(101, 123, 13009)-Net over F4 — Digital
Digital (101, 123, 13009)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4123, 13009, F4, 22) (dual of [13009, 12886, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4123, 16422, F4, 22) (dual of [16422, 16299, 23]-code), using
- 3 times code embedding in larger space [i] based on linear OA(4120, 16419, F4, 22) (dual of [16419, 16299, 23]-code), using
- construction X applied to Ce(21) ⊂ Ce(16) [i] based on
- linear OA(4113, 16384, F4, 22) (dual of [16384, 16271, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(485, 16384, F4, 17) (dual of [16384, 16299, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(21) ⊂ Ce(16) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(4120, 16419, F4, 22) (dual of [16419, 16299, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(4123, 16422, F4, 22) (dual of [16422, 16299, 23]-code), using
(101, 123, large)-Net in Base 4 — Upper bound on s
There is no (101, 123, large)-net in base 4, because
- 20 times m-reduction [i] would yield (101, 103, large)-net in base 4, but