Best Known (202, 202+14, s)-Nets in Base 4
(202, 202+14, 6191588)-Net over F4 — Constructive and digital
Digital (202, 216, 6191588)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (49, 56, 1398104)-net over F4, using
- net defined by OOA [i] based on linear OOA(456, 1398104, F4, 7, 7) (dual of [(1398104, 7), 9786672, 8]-NRT-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(456, 4194313, F4, 7) (dual of [4194313, 4194257, 8]-code), using
- discarding factors / shortening the dual code based on linear OA(456, 4194315, F4, 7) (dual of [4194315, 4194259, 8]-code), using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- linear OA(456, 4194304, F4, 7) (dual of [4194304, 4194248, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(445, 4194304, F4, 6) (dual of [4194304, 4194259, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 4194303 = 411−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(40, 11, F4, 0) (dual of [11, 11, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(40, s, F4, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(6) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(456, 4194315, F4, 7) (dual of [4194315, 4194259, 8]-code), using
- OOA 3-folding and stacking with additional row [i] based on linear OA(456, 4194313, F4, 7) (dual of [4194313, 4194257, 8]-code), using
- net defined by OOA [i] based on linear OOA(456, 1398104, F4, 7, 7) (dual of [(1398104, 7), 9786672, 8]-NRT-code), using
- digital (146, 160, 4793484)-net over F4, using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- discarding factors / shortening the dual code based on linear OA(25640, large, F256, 14) (dual of [large, large−40, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(25640, 8388597, F256, 14) (dual of [8388597, 8388557, 15]-code), using
- net defined by OOA [i] based on linear OOA(25640, 1198371, F256, 14, 14) (dual of [(1198371, 14), 16777154, 15]-NRT-code), using
- trace code for nets [i] based on digital (26, 40, 1198371)-net over F256, using
- digital (49, 56, 1398104)-net over F4, using
(202, 202+14, large)-Net over F4 — Digital
Digital (202, 216, large)-net over F4, using
- t-expansion [i] based on digital (195, 216, large)-net over F4, using
- 1 times m-reduction [i] based on digital (195, 217, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4217, large, F4, 22) (dual of [large, large−217, 23]-code), using
- strength reduction [i] based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- strength reduction [i] based on linear OA(4217, large, F4, 25) (dual of [large, large−217, 26]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4217, large, F4, 22) (dual of [large, large−217, 23]-code), using
- 1 times m-reduction [i] based on digital (195, 217, large)-net over F4, using
(202, 202+14, large)-Net in Base 4 — Upper bound on s
There is no (202, 216, large)-net in base 4, because
- 12 times m-reduction [i] would yield (202, 204, large)-net in base 4, but