Best Known (175, 175+29, s)-Nets in Base 3
(175, 175+29, 4221)-Net over F3 — Constructive and digital
Digital (175, 204, 4221)-net over F3, using
- 32 times duplication [i] based on digital (173, 202, 4221)-net over F3, using
- net defined by OOA [i] based on linear OOA(3202, 4221, F3, 29, 29) (dual of [(4221, 29), 122207, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3202, 59095, F3, 29) (dual of [59095, 58893, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(3202, 59100, F3, 29) (dual of [59100, 58898, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(3191, 59049, F3, 29) (dual of [59049, 58858, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3151, 59049, F3, 23) (dual of [59049, 58898, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(28) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(3202, 59100, F3, 29) (dual of [59100, 58898, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(3202, 59095, F3, 29) (dual of [59095, 58893, 30]-code), using
- net defined by OOA [i] based on linear OOA(3202, 4221, F3, 29, 29) (dual of [(4221, 29), 122207, 30]-NRT-code), using
(175, 175+29, 26836)-Net over F3 — Digital
Digital (175, 204, 26836)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3204, 26836, F3, 2, 29) (dual of [(26836, 2), 53468, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3204, 29551, F3, 2, 29) (dual of [(29551, 2), 58898, 30]-NRT-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3202, 29550, F3, 2, 29) (dual of [(29550, 2), 58898, 30]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3202, 59100, F3, 29) (dual of [59100, 58898, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(22) [i] based on
- linear OA(3191, 59049, F3, 29) (dual of [59049, 58858, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- linear OA(3151, 59049, F3, 23) (dual of [59049, 58898, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [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(28) ⊂ Ce(22) [i] based on
- OOA 2-folding [i] based on linear OA(3202, 59100, F3, 29) (dual of [59100, 58898, 30]-code), using
- 1 times NRT-code embedding in larger space [i] based on linear OOA(3202, 29550, F3, 2, 29) (dual of [(29550, 2), 58898, 30]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3204, 29551, F3, 2, 29) (dual of [(29551, 2), 58898, 30]-NRT-code), using
(175, 175+29, large)-Net in Base 3 — Upper bound on s
There is no (175, 204, large)-net in base 3, because
- 27 times m-reduction [i] would yield (175, 177, large)-net in base 3, but