Best Known (201−19, 201, s)-Nets in Base 4
(201−19, 201, 932323)-Net over F4 — Constructive and digital
Digital (182, 201, 932323)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (23, 32, 257)-net over F4, using
- net defined by OOA [i] based on linear OOA(432, 257, F4, 9, 9) (dual of [(257, 9), 2281, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(432, 1029, F4, 9) (dual of [1029, 997, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(432, 1030, F4, 9) (dual of [1030, 998, 10]-code), using
- construction X applied to Ce(8) ⊂ Ce(6) [i] based on
- linear OA(431, 1024, F4, 9) (dual of [1024, 993, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(426, 1024, F4, 7) (dual of [1024, 998, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 1023 = 45−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(41, 6, F4, 1) (dual of [6, 5, 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(8) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(432, 1030, F4, 9) (dual of [1030, 998, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(432, 1029, F4, 9) (dual of [1029, 997, 10]-code), using
- net defined by OOA [i] based on linear OOA(432, 257, F4, 9, 9) (dual of [(257, 9), 2281, 10]-NRT-code), using
- digital (150, 169, 932066)-net over F4, using
- net defined by OOA [i] based on linear OOA(4169, 932066, F4, 19, 19) (dual of [(932066, 19), 17709085, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4169, 8388595, F4, 19) (dual of [8388595, 8388426, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 16777217 | 424−1, defining interval I = [0,9], and minimum distance d ≥ |{−9,−8,…,9}|+1 = 20 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(4169, large, F4, 19) (dual of [large, large−169, 20]-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(4169, 8388595, F4, 19) (dual of [8388595, 8388426, 20]-code), using
- net defined by OOA [i] based on linear OOA(4169, 932066, F4, 19, 19) (dual of [(932066, 19), 17709085, 20]-NRT-code), using
- digital (23, 32, 257)-net over F4, using
(201−19, 201, large)-Net over F4 — Digital
Digital (182, 201, large)-net over F4, using
- 44 times duplication [i] based on digital (178, 197, large)-net over F4, using
- t-expansion [i] based on digital (177, 197, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- the primitive narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- 17 times code embedding in larger space [i] based on linear OA(4180, large, F4, 20) (dual of [large, large−180, 21]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4197, large, F4, 20) (dual of [large, large−197, 21]-code), using
- t-expansion [i] based on digital (177, 197, large)-net over F4, using
(201−19, 201, large)-Net in Base 4 — Upper bound on s
There is no (182, 201, large)-net in base 4, because
- 17 times m-reduction [i] would yield (182, 184, large)-net in base 4, but