Best Known (205, 205+26, s)-Nets in Base 4
(205, 205+26, 645277)-Net over F4 — Constructive and digital
Digital (205, 231, 645277)-net over F4, using
- 42 times duplication [i] based on digital (203, 229, 645277)-net over F4, using
- net defined by OOA [i] based on linear OOA(4229, 645277, F4, 26, 26) (dual of [(645277, 26), 16776973, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(4229, 8388601, F4, 26) (dual of [8388601, 8388372, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(4229, 8388601, F4, 26) (dual of [8388601, 8388372, 27]-code), using
- net defined by OOA [i] based on linear OOA(4229, 645277, F4, 26, 26) (dual of [(645277, 26), 16776973, 27]-NRT-code), using
(205, 205+26, 3102815)-Net over F4 — Digital
Digital (205, 231, 3102815)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4231, 3102815, F4, 2, 26) (dual of [(3102815, 2), 6205399, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4231, 4194302, F4, 2, 26) (dual of [(4194302, 2), 8388373, 27]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4229, 4194301, F4, 2, 26) (dual of [(4194301, 2), 8388373, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4229, 8388602, F4, 26) (dual of [8388602, 8388373, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,25], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- OOA 2-folding [i] based on linear OA(4229, 8388602, F4, 26) (dual of [8388602, 8388373, 27]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(4229, 4194301, F4, 2, 26) (dual of [(4194301, 2), 8388373, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4231, 4194302, F4, 2, 26) (dual of [(4194302, 2), 8388373, 27]-NRT-code), using
(205, 205+26, large)-Net in Base 4 — Upper bound on s
There is no (205, 231, large)-net in base 4, because
- 24 times m-reduction [i] would yield (205, 207, large)-net in base 4, but