Best Known (129−23, 129, s)-Nets in Base 4
(129−23, 129, 1492)-Net over F4 — Constructive and digital
Digital (106, 129, 1492)-net over F4, using
- 42 times duplication [i] based on digital (104, 127, 1492)-net over F4, using
- net defined by OOA [i] based on linear OOA(4127, 1492, F4, 23, 23) (dual of [(1492, 23), 34189, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4127, 16413, F4, 23) (dual of [16413, 16286, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4127, 16419, F4, 23) (dual of [16419, 16292, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(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(22) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(4127, 16419, F4, 23) (dual of [16419, 16292, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(4127, 16413, F4, 23) (dual of [16413, 16286, 24]-code), using
- net defined by OOA [i] based on linear OOA(4127, 1492, F4, 23, 23) (dual of [(1492, 23), 34189, 24]-NRT-code), using
(129−23, 129, 13506)-Net over F4 — Digital
Digital (106, 129, 13506)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4129, 13506, F4, 23) (dual of [13506, 13377, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4129, 16421, F4, 23) (dual of [16421, 16292, 24]-code), using
- 2 times code embedding in larger space [i] based on linear OA(4127, 16419, F4, 23) (dual of [16419, 16292, 24]-code), using
- construction X applied to Ce(22) ⊂ Ce(17) [i] based on
- linear OA(4120, 16384, F4, 23) (dual of [16384, 16264, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 16383 = 47−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(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(22) ⊂ Ce(17) [i] based on
- 2 times code embedding in larger space [i] based on linear OA(4127, 16419, F4, 23) (dual of [16419, 16292, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(4129, 16421, F4, 23) (dual of [16421, 16292, 24]-code), using
(129−23, 129, large)-Net in Base 4 — Upper bound on s
There is no (106, 129, large)-net in base 4, because
- 21 times m-reduction [i] would yield (106, 108, large)-net in base 4, but