Best Known (250−28, 250, s)-Nets in Base 3
(250−28, 250, 113887)-Net over F3 — Constructive and digital
Digital (222, 250, 113887)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 15, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (207, 235, 113880)-net over F3, using
- net defined by OOA [i] based on linear OOA(3235, 113880, F3, 28, 28) (dual of [(113880, 28), 3188405, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3235, 1594320, F3, 28) (dual of [1594320, 1594085, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3235, 1594323, F3, 28) (dual of [1594323, 1594088, 29]-code), using
- an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- discarding factors / shortening the dual code based on linear OA(3235, 1594323, F3, 28) (dual of [1594323, 1594088, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3235, 1594320, F3, 28) (dual of [1594320, 1594085, 29]-code), using
- net defined by OOA [i] based on linear OOA(3235, 113880, F3, 28, 28) (dual of [(113880, 28), 3188405, 29]-NRT-code), using
- digital (1, 15, 7)-net over F3, using
(250−28, 250, 398732)-Net over F3 — Digital
Digital (222, 250, 398732)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3250, 398732, F3, 3, 28) (dual of [(398732, 3), 1195946, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3250, 531463, F3, 3, 28) (dual of [(531463, 3), 1594139, 29]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3249, 531463, F3, 3, 28) (dual of [(531463, 3), 1594140, 29]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3246, 531462, F3, 3, 28) (dual of [(531462, 3), 1594140, 29]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3246, 1594386, F3, 28) (dual of [1594386, 1594140, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- linear OA(3235, 1594323, F3, 28) (dual of [1594323, 1594088, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(3183, 1594323, F3, 22) (dual of [1594323, 1594140, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(311, 63, F3, 5) (dual of [63, 52, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(311, 85, F3, 5) (dual of [85, 74, 6]-code), using
- construction X applied to Ce(27) ⊂ Ce(21) [i] based on
- OOA 3-folding [i] based on linear OA(3246, 1594386, F3, 28) (dual of [1594386, 1594140, 29]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3246, 531462, F3, 3, 28) (dual of [(531462, 3), 1594140, 29]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3249, 531463, F3, 3, 28) (dual of [(531463, 3), 1594140, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3250, 531463, F3, 3, 28) (dual of [(531463, 3), 1594139, 29]-NRT-code), using
(250−28, 250, large)-Net in Base 3 — Upper bound on s
There is no (222, 250, large)-net in base 3, because
- 26 times m-reduction [i] would yield (222, 224, large)-net in base 3, but