Best Known (183, 208, s)-Nets in Base 4
(183, 208, 349528)-Net over F4 — Constructive and digital
Digital (183, 208, 349528)-net over F4, using
- 44 times duplication [i] based on digital (179, 204, 349528)-net over F4, using
- net defined by OOA [i] based on linear OOA(4204, 349528, F4, 25, 25) (dual of [(349528, 25), 8737996, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4204, 4194337, F4, 25) (dual of [4194337, 4194133, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4204, 4194342, F4, 25) (dual of [4194342, 4194138, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(20) [i] based on
- linear OA(4199, 4194304, F4, 25) (dual of [4194304, 4194105, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(4166, 4194304, F4, 21) (dual of [4194304, 4194138, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(45, 38, F4, 3) (dual of [38, 33, 4]-code or 38-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
- discarding factors / shortening the dual code based on linear OA(4204, 4194342, F4, 25) (dual of [4194342, 4194138, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4204, 4194337, F4, 25) (dual of [4194337, 4194133, 26]-code), using
- net defined by OOA [i] based on linear OOA(4204, 349528, F4, 25, 25) (dual of [(349528, 25), 8737996, 26]-NRT-code), using
(183, 208, 1398118)-Net over F4 — Digital
Digital (183, 208, 1398118)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4208, 1398118, F4, 3, 25) (dual of [(1398118, 3), 4194146, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4208, 4194354, F4, 25) (dual of [4194354, 4194146, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4208, 4194356, F4, 25) (dual of [4194356, 4194148, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- linear OA(4199, 4194305, F4, 25) (dual of [4194305, 4194106, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(4155, 4194305, F4, 19) (dual of [4194305, 4194150, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 4194305 | 422−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- linear OA(49, 51, F4, 5) (dual of [51, 42, 6]-code), using
- a “DaH†code from Brouwer’s database [i]
- construction X applied to C([0,12]) ⊂ C([0,9]) [i] based on
- discarding factors / shortening the dual code based on linear OA(4208, 4194356, F4, 25) (dual of [4194356, 4194148, 26]-code), using
- OOA 3-folding [i] based on linear OA(4208, 4194354, F4, 25) (dual of [4194354, 4194146, 26]-code), using
(183, 208, large)-Net in Base 4 — Upper bound on s
There is no (183, 208, large)-net in base 4, because
- 23 times m-reduction [i] would yield (183, 185, large)-net in base 4, but