Best Known (207−30, 207, s)-Nets in Base 3
(207−30, 207, 3939)-Net over F3 — Constructive and digital
Digital (177, 207, 3939)-net over F3, using
- net defined by OOA [i] based on linear OOA(3207, 3939, F3, 30, 30) (dual of [(3939, 30), 117963, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(3207, 59085, F3, 30) (dual of [59085, 58878, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- OA 15-folding and stacking [i] based on linear OA(3207, 59085, F3, 30) (dual of [59085, 58878, 31]-code), using
(207−30, 207, 22881)-Net over F3 — Digital
Digital (177, 207, 22881)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3207, 22881, F3, 2, 30) (dual of [(22881, 2), 45555, 31]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3207, 29542, F3, 2, 30) (dual of [(29542, 2), 58877, 31]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3207, 59084, F3, 30) (dual of [59084, 58877, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(3207, 59085, F3, 30) (dual of [59085, 58878, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(3201, 59049, F3, 31) (dual of [59049, 58848, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 59048 = 310−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- 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(36, 36, F3, 3) (dual of [36, 30, 4]-code or 36-cap in PG(5,3)), using
- discarding factors / shortening the dual code based on linear OA(36, 48, F3, 3) (dual of [48, 42, 4]-code or 48-cap in PG(5,3)), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(3207, 59085, F3, 30) (dual of [59085, 58878, 31]-code), using
- OOA 2-folding [i] based on linear OA(3207, 59084, F3, 30) (dual of [59084, 58877, 31]-code), using
- discarding factors / shortening the dual code based on linear OOA(3207, 29542, F3, 2, 30) (dual of [(29542, 2), 58877, 31]-NRT-code), using
(207−30, 207, large)-Net in Base 3 — Upper bound on s
There is no (177, 207, large)-net in base 3, because
- 28 times m-reduction [i] would yield (177, 179, large)-net in base 3, but