Best Known (205, 235, s)-Nets in Base 4
(205, 235, 69909)-Net over F4 — Constructive and digital
Digital (205, 235, 69909)-net over F4, using
- 41 times duplication [i] based on digital (204, 234, 69909)-net over F4, using
- net defined by OOA [i] based on linear OOA(4234, 69909, F4, 30, 30) (dual of [(69909, 30), 2097036, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(4234, 1048635, F4, 30) (dual of [1048635, 1048401, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(4234, 1048639, F4, 30) (dual of [1048639, 1048405, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(4234, 1048639, F4, 30) (dual of [1048639, 1048405, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(4234, 1048635, F4, 30) (dual of [1048635, 1048401, 31]-code), using
- net defined by OOA [i] based on linear OOA(4234, 69909, F4, 30, 30) (dual of [(69909, 30), 2097036, 31]-NRT-code), using
(205, 235, 524320)-Net over F4 — Digital
Digital (205, 235, 524320)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4235, 524320, F4, 2, 30) (dual of [(524320, 2), 1048405, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4235, 1048640, F4, 30) (dual of [1048640, 1048405, 31]-code), using
- 1 times code embedding in larger space [i] based on linear OA(4234, 1048639, F4, 30) (dual of [1048639, 1048405, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- linear OA(4221, 1048576, F4, 30) (dual of [1048576, 1048355, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(4171, 1048576, F4, 23) (dual of [1048576, 1048405, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 410−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(413, 63, F4, 6) (dual of [63, 50, 7]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 63 = 43−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(4234, 1048639, F4, 30) (dual of [1048639, 1048405, 31]-code), using
- OOA 2-folding [i] based on linear OA(4235, 1048640, F4, 30) (dual of [1048640, 1048405, 31]-code), using
(205, 235, large)-Net in Base 4 — Upper bound on s
There is no (205, 235, large)-net in base 4, because
- 28 times m-reduction [i] would yield (205, 207, large)-net in base 4, but