Best Known (200−21, 200, s)-Nets in Base 4
(200−21, 200, 838883)-Net over F4 — Constructive and digital
Digital (179, 200, 838883)-net over F4, using
- (u, u+v)-construction [i] based on
- digital (9, 19, 23)-net over F4, using
- 4 times m-reduction [i] based on digital (9, 23, 23)-net over F4, using
- digital (160, 181, 838860)-net over F4, using
- net defined by OOA [i] based on linear OOA(4181, 838860, F4, 21, 21) (dual of [(838860, 21), 17615879, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4181, 8388601, F4, 21) (dual of [8388601, 8388420, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(4181, 8388601, F4, 21) (dual of [8388601, 8388420, 22]-code), using
- net defined by OOA [i] based on linear OOA(4181, 838860, F4, 21, 21) (dual of [(838860, 21), 17615879, 22]-NRT-code), using
- digital (9, 19, 23)-net over F4, using
(200−21, 200, 5344158)-Net over F4 — Digital
Digital (179, 200, 5344158)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4200, 5344158, F4, 21) (dual of [5344158, 5343958, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4200, large, F4, 21) (dual of [large, large−200, 22]-code), using
- 19 times code embedding in larger space [i] based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 412−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 19 times code embedding in larger space [i] based on linear OA(4181, large, F4, 21) (dual of [large, large−181, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(4200, large, F4, 21) (dual of [large, large−200, 22]-code), using
(200−21, 200, large)-Net in Base 4 — Upper bound on s
There is no (179, 200, large)-net in base 4, because
- 19 times m-reduction [i] would yield (179, 181, large)-net in base 4, but