Best Known (201, 201+34, s)-Nets in Base 4
(201, 201+34, 15422)-Net over F4 — Constructive and digital
Digital (201, 235, 15422)-net over F4, using
- 44 times duplication [i] based on digital (197, 231, 15422)-net over F4, using
- net defined by OOA [i] based on linear OOA(4231, 15422, F4, 34, 34) (dual of [(15422, 34), 524117, 35]-NRT-code), using
- OA 17-folding and stacking [i] based on linear OA(4231, 262174, F4, 34) (dual of [262174, 261943, 35]-code), using
- discarding factors / shortening the dual code based on linear OA(4231, 262176, F4, 34) (dual of [262176, 261945, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(29) [i] based on
- linear OA(4226, 262144, F4, 34) (dual of [262144, 261918, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4199, 262144, F4, 30) (dual of [262144, 261945, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(45, 32, F4, 3) (dual of [32, 27, 4]-code or 32-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(33) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(4231, 262176, F4, 34) (dual of [262176, 261945, 35]-code), using
- OA 17-folding and stacking [i] based on linear OA(4231, 262174, F4, 34) (dual of [262174, 261943, 35]-code), using
- net defined by OOA [i] based on linear OOA(4231, 15422, F4, 34, 34) (dual of [(15422, 34), 524117, 35]-NRT-code), using
(201, 201+34, 131094)-Net over F4 — Digital
Digital (201, 235, 131094)-net over F4, using
- 41 times duplication [i] based on digital (200, 234, 131094)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4234, 131094, F4, 2, 34) (dual of [(131094, 2), 261954, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4234, 262188, F4, 34) (dual of [262188, 261954, 35]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4233, 262187, F4, 34) (dual of [262187, 261954, 35]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- linear OA(4226, 262144, F4, 34) (dual of [262144, 261918, 35]-code), using an extension Ce(33) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,33], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(4190, 262144, F4, 29) (dual of [262144, 261954, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 262143 = 49−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(47, 43, F4, 4) (dual of [43, 36, 5]-code), using
- construction X applied to Ce(33) ⊂ Ce(28) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4233, 262187, F4, 34) (dual of [262187, 261954, 35]-code), using
- OOA 2-folding [i] based on linear OA(4234, 262188, F4, 34) (dual of [262188, 261954, 35]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4234, 131094, F4, 2, 34) (dual of [(131094, 2), 261954, 35]-NRT-code), using
(201, 201+34, large)-Net in Base 4 — Upper bound on s
There is no (201, 235, large)-net in base 4, because
- 32 times m-reduction [i] would yield (201, 203, large)-net in base 4, but