Best Known (155−26, 155, s)-Nets in Base 3
(155−26, 155, 1514)-Net over F3 — Constructive and digital
Digital (129, 155, 1514)-net over F3, using
- 31 times duplication [i] based on digital (128, 154, 1514)-net over F3, using
- net defined by OOA [i] based on linear OOA(3154, 1514, F3, 26, 26) (dual of [(1514, 26), 39210, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(3154, 19682, F3, 26) (dual of [19682, 19528, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using
- an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- discarding factors / shortening the dual code based on linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(3154, 19682, F3, 26) (dual of [19682, 19528, 27]-code), using
- net defined by OOA [i] based on linear OOA(3154, 1514, F3, 26, 26) (dual of [(1514, 26), 39210, 27]-NRT-code), using
(155−26, 155, 7014)-Net over F3 — Digital
Digital (129, 155, 7014)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3155, 7014, F3, 2, 26) (dual of [(7014, 2), 13873, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3155, 9846, F3, 2, 26) (dual of [(9846, 2), 19537, 27]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3154, 9846, F3, 2, 26) (dual of [(9846, 2), 19538, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3154, 19692, F3, 26) (dual of [19692, 19538, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(3154, 19683, F3, 26) (dual of [19683, 19529, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 19682 = 39−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 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(30, 9, F3, 0) (dual of [9, 9, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(30, s, F3, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- OOA 2-folding [i] based on linear OA(3154, 19692, F3, 26) (dual of [19692, 19538, 27]-code), using
- 31 times duplication [i] based on linear OOA(3154, 9846, F3, 2, 26) (dual of [(9846, 2), 19538, 27]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3155, 9846, F3, 2, 26) (dual of [(9846, 2), 19537, 27]-NRT-code), using
(155−26, 155, 1383966)-Net in Base 3 — Upper bound on s
There is no (129, 155, 1383967)-net in base 3, because
- the generalized Rao bound for nets shows that 3m ≥ 89 907344 636421 315425 928857 658887 938005 742001 314423 610620 383102 043939 953447 > 3155 [i]