Best Known (196−21, 196, s)-Nets in Base 3
(196−21, 196, 478296)-Net over F3 — Constructive and digital
Digital (175, 196, 478296)-net over F3, using
- net defined by OOA [i] based on linear OOA(3196, 478296, F3, 21, 21) (dual of [(478296, 21), 10044020, 22]-NRT-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3196, 4782961, F3, 21) (dual of [4782961, 4782765, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, 4782968, F3, 21) (dual of [4782968, 4782772, 22]-code), using
- 1 times truncation [i] based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 1 times truncation [i] based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(3196, 4782968, F3, 21) (dual of [4782968, 4782772, 22]-code), using
- OOA 10-folding and stacking with additional row [i] based on linear OA(3196, 4782961, F3, 21) (dual of [4782961, 4782765, 22]-code), using
(196−21, 196, 1195742)-Net over F3 — Digital
Digital (175, 196, 1195742)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3196, 1195742, F3, 4, 21) (dual of [(1195742, 4), 4782772, 22]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3196, 4782968, F3, 21) (dual of [4782968, 4782772, 22]-code), using
- 1 times truncation [i] based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- 1 times truncation [i] based on linear OA(3197, 4782969, F3, 22) (dual of [4782969, 4782772, 23]-code), using
- OOA 4-folding [i] based on linear OA(3196, 4782968, F3, 21) (dual of [4782968, 4782772, 22]-code), using
(196−21, 196, large)-Net in Base 3 — Upper bound on s
There is no (175, 196, large)-net in base 3, because
- 19 times m-reduction [i] would yield (175, 177, large)-net in base 3, but