Best Known (248−26, 248, s)-Nets in Base 3
(248−26, 248, 367924)-Net over F3 — Constructive and digital
Digital (222, 248, 367924)-net over F3, using
- 33 times duplication [i] based on digital (219, 245, 367924)-net over F3, using
- net defined by OOA [i] based on linear OOA(3245, 367924, F3, 26, 26) (dual of [(367924, 26), 9565779, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3245, 4783012, F3, 26) (dual of [4783012, 4782767, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3245, 4783017, F3, 26) (dual of [4783017, 4782772, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(3239, 4782969, F3, 26) (dual of [4782969, 4782730, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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]
- 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(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(3245, 4783017, F3, 26) (dual of [4783017, 4782772, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3245, 4783012, F3, 26) (dual of [4783012, 4782767, 27]-code), using
- net defined by OOA [i] based on linear OOA(3245, 367924, F3, 26, 26) (dual of [(367924, 26), 9565779, 27]-NRT-code), using
(248−26, 248, 1195755)-Net over F3 — Digital
Digital (222, 248, 1195755)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3248, 1195755, F3, 4, 26) (dual of [(1195755, 4), 4782772, 27]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3248, 4783020, F3, 26) (dual of [4783020, 4782772, 27]-code), using
- 3 times code embedding in larger space [i] based on linear OA(3245, 4783017, F3, 26) (dual of [4783017, 4782772, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(3239, 4782969, F3, 26) (dual of [4782969, 4782730, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 314−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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]
- 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(25) ⊂ Ce(21) [i] based on
- 3 times code embedding in larger space [i] based on linear OA(3245, 4783017, F3, 26) (dual of [4783017, 4782772, 27]-code), using
- OOA 4-folding [i] based on linear OA(3248, 4783020, F3, 26) (dual of [4783020, 4782772, 27]-code), using
(248−26, 248, large)-Net in Base 3 — Upper bound on s
There is no (222, 248, large)-net in base 3, because
- 24 times m-reduction [i] would yield (222, 224, large)-net in base 3, but