Best Known (109, 109+11, s)-Nets in Base 3
(109, 109+11, 1677823)-Net over F3 — Constructive and digital
Digital (109, 120, 1677823)-net over F3, using
- 31 times duplication [i] based on digital (108, 119, 1677823)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 103)-net over F3, 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
- (u, u+v)-construction [i] based on
(109, 109+11, 4220111)-Net over F3 — Digital
Digital (109, 120, 4220111)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3120, 4220111, F3, 11) (dual of [4220111, 4219991, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 11) (dual of [large, large−120, 12]-code), using
- strength reduction [i] based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- strength reduction [i] based on linear OA(3120, large, F3, 12) (dual of [large, large−120, 13]-code), using
- discarding factors / shortening the dual code based on linear OA(3120, large, F3, 11) (dual of [large, large−120, 12]-code), using
(109, 109+11, large)-Net in Base 3 — Upper bound on s
There is no (109, 120, large)-net in base 3, because
- 9 times m-reduction [i] would yield (109, 111, large)-net in base 3, but