Best Known (130, 130+24, s)-Nets in Base 4
(130, 130+24, 5464)-Net over F4 — Constructive and digital
Digital (130, 154, 5464)-net over F4, using
- 41 times duplication [i] based on digital (129, 153, 5464)-net over F4, using
- t-expansion [i] based on digital (128, 153, 5464)-net over F4, using
- net defined by OOA [i] based on linear OOA(4153, 5464, F4, 25, 25) (dual of [(5464, 25), 136447, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4153, 65569, F4, 25) (dual of [65569, 65416, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4153, 65570, F4, 25) (dual of [65570, 65417, 26]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- linear OA(4145, 65536, F4, 25) (dual of [65536, 65391, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4121, 65536, F4, 21) (dual of [65536, 65415, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(4113, 65536, F4, 19) (dual of [65536, 65423, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 65535 = 48−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(45, 31, F4, 3) (dual of [31, 26, 4]-code or 31-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(41, 3, F4, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- Reed–Solomon code RS(3,4) [i]
- discarding factors / shortening the dual code based on linear OA(41, 4, F4, 1) (dual of [4, 3, 2]-code), using
- construction XX applied to Ce(24) ⊂ Ce(20) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(4153, 65570, F4, 25) (dual of [65570, 65417, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4153, 65569, F4, 25) (dual of [65569, 65416, 26]-code), using
- net defined by OOA [i] based on linear OOA(4153, 5464, F4, 25, 25) (dual of [(5464, 25), 136447, 26]-NRT-code), using
- t-expansion [i] based on digital (128, 153, 5464)-net over F4, using
(130, 130+24, 46411)-Net over F4 — Digital
Digital (130, 154, 46411)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4154, 46411, F4, 24) (dual of [46411, 46257, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(4154, 65578, F4, 24) (dual of [65578, 65424, 25]-code), using
- 1 times truncation [i] based on linear OA(4155, 65579, F4, 25) (dual of [65579, 65424, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4145, 65537, F4, 25) (dual of [65537, 65392, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4113, 65537, F4, 19) (dual of [65537, 65424, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 65537 | 416−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(410, 42, F4, 5) (dual of [42, 32, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,3], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(410, 63, F4, 5) (dual of [63, 53, 6]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- 1 times truncation [i] based on linear OA(4155, 65579, F4, 25) (dual of [65579, 65424, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4154, 65578, F4, 24) (dual of [65578, 65424, 25]-code), using
(130, 130+24, large)-Net in Base 4 — Upper bound on s
There is no (130, 154, large)-net in base 4, because
- 22 times m-reduction [i] would yield (130, 132, large)-net in base 4, but