Best Known (208, 234, s)-Nets in Base 4
(208, 234, 645277)-Net over F4 — Constructive and digital
Digital (208, 234, 645277)-net over F4, using
- 45 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
(208, 234, 3717799)-Net over F4 — Digital
Digital (208, 234, 3717799)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4234, 3717799, F4, 2, 26) (dual of [(3717799, 2), 7435364, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4234, 4194303, F4, 2, 26) (dual of [(4194303, 2), 8388372, 27]-NRT-code), using
- 41 times duplication [i] based on linear OOA(4233, 4194303, F4, 2, 26) (dual of [(4194303, 2), 8388373, 27]-NRT-code), using
- 2 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
- 2 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
- 41 times duplication [i] based on linear OOA(4233, 4194303, F4, 2, 26) (dual of [(4194303, 2), 8388373, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4234, 4194303, F4, 2, 26) (dual of [(4194303, 2), 8388372, 27]-NRT-code), using
(208, 234, large)-Net in Base 4 — Upper bound on s
There is no (208, 234, large)-net in base 4, because
- 24 times m-reduction [i] would yield (208, 210, large)-net in base 4, but