Best Known (225−25, 225, s)-Nets in Base 3
(225−25, 225, 398580)-Net over F3 — Constructive and digital
Digital (200, 225, 398580)-net over F3, using
- net defined by OOA [i] based on linear OOA(3225, 398580, F3, 25, 25) (dual of [(398580, 25), 9964275, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3225, 4782961, F3, 25) (dual of [4782961, 4782736, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using
- an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- discarding factors / shortening the dual code based on linear OA(3225, 4782969, F3, 25) (dual of [4782969, 4782744, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3225, 4782961, F3, 25) (dual of [4782961, 4782736, 26]-code), using
(225−25, 225, 956594)-Net over F3 — Digital
Digital (200, 225, 956594)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3225, 956594, F3, 5, 25) (dual of [(956594, 5), 4782745, 26]-NRT-code), using
- OOA 5-folding [i] based on linear OA(3225, 4782970, F3, 25) (dual of [4782970, 4782745, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4782970 | 328−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- OOA 5-folding [i] based on linear OA(3225, 4782970, F3, 25) (dual of [4782970, 4782745, 26]-code), using
(225−25, 225, large)-Net in Base 3 — Upper bound on s
There is no (200, 225, large)-net in base 3, because
- 23 times m-reduction [i] would yield (200, 202, large)-net in base 3, but