Best Known (233, 233+22, s)-Nets in Base 4
(233, 233+22, 2287800)-Net over F4 — Constructive and digital
Digital (233, 255, 2287800)-net over F4, using
- trace code for nets [i] based on digital (63, 85, 762600)-net over F64, using
- net defined by OOA [i] based on linear OOA(6485, 762600, F64, 22, 22) (dual of [(762600, 22), 16777115, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(6485, 8388600, F64, 22) (dual of [8388600, 8388515, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 644−1, defining interval I = [0,21], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(6485, large, F64, 22) (dual of [large, large−85, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(6485, 8388600, F64, 22) (dual of [8388600, 8388515, 23]-code), using
- net defined by OOA [i] based on linear OOA(6485, 762600, F64, 22, 22) (dual of [(762600, 22), 16777115, 23]-NRT-code), using
(233, 233+22, large)-Net over F4 — Digital
Digital (233, 255, large)-net over F4, using
- t-expansion [i] based on digital (231, 255, large)-net over F4, using
- 2 times m-reduction [i] based on digital (231, 257, large)-net over F4, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4257, large, F4, 26) (dual of [large, large−257, 27]-code), using
- 28 times code embedding in larger space [i] 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]
- 28 times code embedding in larger space [i] based on linear OA(4229, large, F4, 26) (dual of [large, large−229, 27]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(4257, large, F4, 26) (dual of [large, large−257, 27]-code), using
- 2 times m-reduction [i] based on digital (231, 257, large)-net over F4, using
(233, 233+22, large)-Net in Base 4 — Upper bound on s
There is no (233, 255, large)-net in base 4, because
- 20 times m-reduction [i] would yield (233, 235, large)-net in base 4, but