Best Known (127−11, 127, s)-Nets in Base 3
(127−11, 127, 1678774)-Net over F3 — Constructive and digital
Digital (116, 127, 1678774)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (16, 21, 1054)-net over F3, using
- net defined by OOA [i] based on linear OOA(321, 1054, F3, 5, 5) (dual of [(1054, 5), 5249, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(321, 2109, F3, 5) (dual of [2109, 2088, 6]-code), using
- trace code [i] based on linear OA(277, 703, F27, 5) (dual of [703, 696, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(321, 2109, F3, 5) (dual of [2109, 2088, 6]-code), using
- net defined by OOA [i] based on linear OOA(321, 1054, F3, 5, 5) (dual of [(1054, 5), 5249, 6]-NRT-code), using
- digital (95, 106, 1677720)-net over F3, using
- net defined by OOA [i] based on linear OOA(3106, 1677720, F3, 11, 11) (dual of [(1677720, 11), 18454814, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3106, 8388601, F3, 11) (dual of [8388601, 8388495, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding factors / shortening the dual code based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(3106, 8388601, F3, 11) (dual of [8388601, 8388495, 12]-code), using
- net defined by OOA [i] based on linear OOA(3106, 1677720, F3, 11, 11) (dual of [(1677720, 11), 18454814, 12]-NRT-code), using
- digital (16, 21, 1054)-net over F3, using
(127−11, 127, large)-Net over F3 — Digital
Digital (116, 127, large)-net over F3, using
- 31 times duplication [i] based on digital (115, 126, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3126, large, F3, 11) (dual of [large, large−126, 12]-code), using
- 20 times code embedding in larger space [i] based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- 20 times code embedding in larger space [i] based on linear OA(3106, large, F3, 11) (dual of [large, large−106, 12]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3126, large, F3, 11) (dual of [large, large−126, 12]-code), using
(127−11, 127, large)-Net in Base 3 — Upper bound on s
There is no (116, 127, large)-net in base 3, because
- 9 times m-reduction [i] would yield (116, 118, large)-net in base 3, but