Best Known (235−26, 235, s)-Nets in Base 3
(235−26, 235, 122645)-Net over F3 — Constructive and digital
Digital (209, 235, 122645)-net over F3, using
- 32 times duplication [i] based on digital (207, 233, 122645)-net over F3, using
- net defined by OOA [i] based on linear OOA(3233, 122645, F3, 26, 26) (dual of [(122645, 26), 3188537, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3233, 1594385, F3, 26) (dual of [1594385, 1594152, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3233, 1594386, F3, 26) (dual of [1594386, 1594153, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- 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(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- discarding factors / shortening the dual code based on linear OA(3233, 1594386, F3, 26) (dual of [1594386, 1594153, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3233, 1594385, F3, 26) (dual of [1594385, 1594152, 27]-code), using
- net defined by OOA [i] based on linear OOA(3233, 122645, F3, 26, 26) (dual of [(122645, 26), 3188537, 27]-NRT-code), using
(235−26, 235, 486704)-Net over F3 — Digital
Digital (209, 235, 486704)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3235, 486704, F3, 3, 26) (dual of [(486704, 3), 1459877, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3235, 531462, F3, 3, 26) (dual of [(531462, 3), 1594151, 27]-NRT-code), using
- 32 times duplication [i] based on linear OOA(3233, 531462, F3, 3, 26) (dual of [(531462, 3), 1594153, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(3233, 1594386, F3, 26) (dual of [1594386, 1594153, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- 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(3170, 1594323, F3, 20) (dual of [1594323, 1594153, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1594322 = 313−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [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(25) ⊂ Ce(19) [i] based on
- OOA 3-folding [i] based on linear OA(3233, 1594386, F3, 26) (dual of [1594386, 1594153, 27]-code), using
- 32 times duplication [i] based on linear OOA(3233, 531462, F3, 3, 26) (dual of [(531462, 3), 1594153, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3235, 531462, F3, 3, 26) (dual of [(531462, 3), 1594151, 27]-NRT-code), using
(235−26, 235, large)-Net in Base 3 — Upper bound on s
There is no (209, 235, large)-net in base 3, because
- 24 times m-reduction [i] would yield (209, 211, large)-net in base 3, but