Best Known (231−24, 231, s)-Nets in Base 3
(231−24, 231, 398584)-Net over F3 — Constructive and digital
Digital (207, 231, 398584)-net over F3, using
- net defined by OOA [i] based on linear OOA(3231, 398584, F3, 24, 24) (dual of [(398584, 24), 9565785, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(3231, 4783008, F3, 24) (dual of [4783008, 4782777, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3231, 4783017, F3, 24) (dual of [4783017, 4782786, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] 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]
- linear OA(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3231, 4783017, F3, 24) (dual of [4783017, 4782786, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(3231, 4783008, F3, 24) (dual of [4783008, 4782777, 25]-code), using
(231−24, 231, 1195754)-Net over F3 — Digital
Digital (207, 231, 1195754)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3231, 1195754, F3, 4, 24) (dual of [(1195754, 4), 4782785, 25]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3231, 4783016, F3, 24) (dual of [4783016, 4782785, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(3231, 4783017, F3, 24) (dual of [4783017, 4782786, 25]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] 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]
- linear OA(3183, 4782969, F3, 20) (dual of [4782969, 4782786, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3231, 4783017, F3, 24) (dual of [4783017, 4782786, 25]-code), using
- OOA 4-folding [i] based on linear OA(3231, 4783016, F3, 24) (dual of [4783016, 4782785, 25]-code), using
(231−24, 231, large)-Net in Base 3 — Upper bound on s
There is no (207, 231, large)-net in base 3, because
- 22 times m-reduction [i] would yield (207, 209, large)-net in base 3, but