Best Known (201−25, 201, s)-Nets in Base 4
(201−25, 201, 349526)-Net over F4 — Constructive and digital
Digital (176, 201, 349526)-net over F4, using
- 41 times duplication [i] based on digital (175, 200, 349526)-net over F4, using
- net defined by OOA [i] based on linear OOA(4200, 349526, F4, 25, 25) (dual of [(349526, 25), 8737950, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4200, 4194313, F4, 25) (dual of [4194313, 4194113, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4200, 4194316, F4, 25) (dual of [4194316, 4194116, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [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(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4200, 4194316, F4, 25) (dual of [4194316, 4194116, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(4200, 4194313, F4, 25) (dual of [4194313, 4194113, 26]-code), using
- net defined by OOA [i] based on linear OOA(4200, 349526, F4, 25, 25) (dual of [(349526, 25), 8737950, 26]-NRT-code), using
(201−25, 201, 1373826)-Net over F4 — Digital
Digital (176, 201, 1373826)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4201, 1373826, F4, 3, 25) (dual of [(1373826, 3), 4121277, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4201, 1398105, F4, 3, 25) (dual of [(1398105, 3), 4194114, 26]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4200, 1398105, F4, 3, 25) (dual of [(1398105, 3), 4194115, 26]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4200, 4194315, F4, 25) (dual of [4194315, 4194115, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(4200, 4194316, F4, 25) (dual of [4194316, 4194116, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(22) [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(4188, 4194304, F4, 23) (dual of [4194304, 4194116, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(41, 12, F4, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(41, s, F4, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(24) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4200, 4194316, F4, 25) (dual of [4194316, 4194116, 26]-code), using
- OOA 3-folding [i] based on linear OA(4200, 4194315, F4, 25) (dual of [4194315, 4194115, 26]-code), using
- 41 times duplication [i] based on linear OOA(4200, 1398105, F4, 3, 25) (dual of [(1398105, 3), 4194115, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4201, 1398105, F4, 3, 25) (dual of [(1398105, 3), 4194114, 26]-NRT-code), using
(201−25, 201, large)-Net in Base 4 — Upper bound on s
There is no (176, 201, large)-net in base 4, because
- 23 times m-reduction [i] would yield (176, 178, large)-net in base 4, but