Best Known (210, 238, s)-Nets in Base 3
(210, 238, 113881)-Net over F3 — Constructive and digital
Digital (210, 238, 113881)-net over F3, using
- 32 times duplication [i] based on digital (208, 236, 113881)-net over F3, using
- net defined by OOA [i] based on linear OOA(3236, 113881, F3, 28, 28) (dual of [(113881, 28), 3188432, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(3236, 1594334, F3, 28) (dual of [1594334, 1594098, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 1594337, F3, 28) (dual of [1594337, 1594101, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [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(3222, 1594323, F3, 26) (dual of [1594323, 1594101, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 1594337, F3, 28) (dual of [1594337, 1594101, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(3236, 1594334, F3, 28) (dual of [1594334, 1594098, 29]-code), using
- net defined by OOA [i] based on linear OOA(3236, 113881, F3, 28, 28) (dual of [(113881, 28), 3188432, 29]-NRT-code), using
(210, 238, 336968)-Net over F3 — Digital
Digital (210, 238, 336968)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3238, 336968, F3, 4, 28) (dual of [(336968, 4), 1347634, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3238, 398584, F3, 4, 28) (dual of [(398584, 4), 1594098, 29]-NRT-code), using
- 32 times duplication [i] based on linear OOA(3236, 398584, F3, 4, 28) (dual of [(398584, 4), 1594100, 29]-NRT-code), using
- OOA 4-folding [i] based on linear OA(3236, 1594336, F3, 28) (dual of [1594336, 1594100, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(3236, 1594337, F3, 28) (dual of [1594337, 1594101, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [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(3222, 1594323, F3, 26) (dual of [1594323, 1594101, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(31, 14, F3, 1) (dual of [14, 13, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(31, s, F3, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3236, 1594337, F3, 28) (dual of [1594337, 1594101, 29]-code), using
- OOA 4-folding [i] based on linear OA(3236, 1594336, F3, 28) (dual of [1594336, 1594100, 29]-code), using
- 32 times duplication [i] based on linear OOA(3236, 398584, F3, 4, 28) (dual of [(398584, 4), 1594100, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3238, 398584, F3, 4, 28) (dual of [(398584, 4), 1594098, 29]-NRT-code), using
(210, 238, large)-Net in Base 3 — Upper bound on s
There is no (210, 238, large)-net in base 3, because
- 26 times m-reduction [i] would yield (210, 212, large)-net in base 3, but