Best Known (127, 152, s)-Nets in Base 3
(127, 152, 1642)-Net over F3 — Constructive and digital
Digital (127, 152, 1642)-net over F3, using
- 33 times duplication [i] based on digital (124, 149, 1642)-net over F3, using
- net defined by OOA [i] based on linear OOA(3149, 1642, F3, 25, 25) (dual of [(1642, 25), 40901, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(3149, 19705, F3, 25) (dual of [19705, 19556, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3127, 19683, F3, 22) (dual of [19683, 19556, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(34, 22, F3, 2) (dual of [22, 18, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- Hamming code H(4,3) [i]
- discarding factors / shortening the dual code based on linear OA(34, 40, F3, 2) (dual of [40, 36, 3]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(3149, 19705, F3, 25) (dual of [19705, 19556, 26]-code), using
- net defined by OOA [i] based on linear OOA(3149, 1642, F3, 25, 25) (dual of [(1642, 25), 40901, 26]-NRT-code), using
(127, 152, 8087)-Net over F3 — Digital
Digital (127, 152, 8087)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3152, 8087, F3, 2, 25) (dual of [(8087, 2), 16022, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3152, 9855, F3, 2, 25) (dual of [(9855, 2), 19558, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3152, 19710, F3, 25) (dual of [19710, 19558, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- linear OA(3145, 19683, F3, 25) (dual of [19683, 19538, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(3118, 19683, F3, 20) (dual of [19683, 19565, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(37, 27, F3, 4) (dual of [27, 20, 5]-code), using
- an extension Ce(3) of the primitive narrow-sense BCH-code C(I) with length 26 = 33−1, defining interval I = [1,3], and designed minimum distance d ≥ |I|+1 = 4 [i]
- construction X applied to Ce(24) ⊂ Ce(19) [i] based on
- OOA 2-folding [i] based on linear OA(3152, 19710, F3, 25) (dual of [19710, 19558, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(3152, 9855, F3, 2, 25) (dual of [(9855, 2), 19558, 26]-NRT-code), using
(127, 152, 2667505)-Net in Base 3 — Upper bound on s
There is no (127, 152, 2667506)-net in base 3, because
- 1 times m-reduction [i] would yield (127, 151, 2667506)-net in base 3, but
- the generalized Rao bound for nets shows that 3m ≥ 1 109967 622998 777891 487609 893843 070222 674806 135540 063216 322574 504561 218169 > 3151 [i]