Best Known (157, 157+26, s)-Nets in Base 3
(157, 157+26, 4546)-Net over F3 — Constructive and digital
Digital (157, 183, 4546)-net over F3, using
- 31 times duplication [i] based on digital (156, 182, 4546)-net over F3, using
- net defined by OOA [i] based on linear OOA(3182, 4546, F3, 26, 26) (dual of [(4546, 26), 118014, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3182, 59098, F3, 26) (dual of [59098, 58916, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3182, 59100, F3, 26) (dual of [59100, 58918, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 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(3182, 59100, F3, 26) (dual of [59100, 58918, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3182, 59098, F3, 26) (dual of [59098, 58916, 27]-code), using
- net defined by OOA [i] based on linear OOA(3182, 4546, F3, 26, 26) (dual of [(4546, 26), 118014, 27]-NRT-code), using
(157, 157+26, 26780)-Net over F3 — Digital
Digital (157, 183, 26780)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3183, 26780, F3, 2, 26) (dual of [(26780, 2), 53377, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3183, 29550, F3, 2, 26) (dual of [(29550, 2), 58917, 27]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3182, 29550, F3, 2, 26) (dual of [(29550, 2), 58918, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3182, 59100, F3, 26) (dual of [59100, 58918, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(19) [i] based on
- linear OA(3171, 59049, F3, 26) (dual of [59049, 58878, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(3131, 59049, F3, 20) (dual of [59049, 58918, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(311, 51, F3, 5) (dual of [51, 40, 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 2-folding [i] based on linear OA(3182, 59100, F3, 26) (dual of [59100, 58918, 27]-code), using
- 31 times duplication [i] based on linear OOA(3182, 29550, F3, 2, 26) (dual of [(29550, 2), 58918, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3183, 29550, F3, 2, 26) (dual of [(29550, 2), 58917, 27]-NRT-code), using
(157, 157+26, large)-Net in Base 3 — Upper bound on s
There is no (157, 183, large)-net in base 3, because
- 24 times m-reduction [i] would yield (157, 159, large)-net in base 3, but