Best Known (20, 20+8, s)-Nets in Base 8
(20, 20+8, 1023)-Net over F8 — Constructive and digital
Digital (20, 28, 1023)-net over F8, using
- net defined by OOA [i] based on linear OOA(828, 1023, F8, 8, 8) (dual of [(1023, 8), 8156, 9]-NRT-code), using
- OA 4-folding and stacking [i] based on linear OA(828, 4092, F8, 8) (dual of [4092, 4064, 9]-code), using
- discarding factors / shortening the dual code based on linear OA(828, 4095, F8, 8) (dual of [4095, 4067, 9]-code), using
- 1 times truncation [i] based on linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 1 times truncation [i] based on linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(828, 4095, F8, 8) (dual of [4095, 4067, 9]-code), using
- OA 4-folding and stacking [i] based on linear OA(828, 4092, F8, 8) (dual of [4092, 4064, 9]-code), using
(20, 20+8, 4095)-Net over F8 — Digital
Digital (20, 28, 4095)-net over F8, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(828, 4095, F8, 8) (dual of [4095, 4067, 9]-code), using
- 1 times truncation [i] based on linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using
- an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 4095 = 84−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- 1 times truncation [i] based on linear OA(829, 4096, F8, 9) (dual of [4096, 4067, 10]-code), using
(20, 20+8, 663106)-Net in Base 8 — Upper bound on s
There is no (20, 28, 663107)-net in base 8, because
- the generalized Rao bound for nets shows that 8m ≥ 19 342864 743882 646319 660112 > 828 [i]