Best Known (103, 103+14, s)-Nets in Base 3
(103, 103+14, 75928)-Net over F3 — Constructive and digital
Digital (103, 117, 75928)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (1, 8, 7)-net over F3, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F3 with g(F) = 1 and N(F) ≥ 7, using
- net from sequence [i] based on digital (1, 6)-sequence over F3, using
- digital (95, 109, 75921)-net over F3, using
- net defined by OOA [i] based on linear OOA(3109, 75921, F3, 14, 14) (dual of [(75921, 14), 1062785, 15]-NRT-code), using
- OA 7-folding and stacking [i] based on linear OA(3109, 531447, F3, 14) (dual of [531447, 531338, 15]-code), using
- discarding factors / shortening the dual code based on linear OA(3109, 531453, F3, 14) (dual of [531453, 531344, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(12) [i] based on
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(397, 531441, F3, 13) (dual of [531441, 531344, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(30, 12, F3, 0) (dual of [12, 12, 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(13) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(3109, 531453, F3, 14) (dual of [531453, 531344, 15]-code), using
- OA 7-folding and stacking [i] based on linear OA(3109, 531447, F3, 14) (dual of [531447, 531338, 15]-code), using
- net defined by OOA [i] based on linear OOA(3109, 75921, F3, 14, 14) (dual of [(75921, 14), 1062785, 15]-NRT-code), using
- digital (1, 8, 7)-net over F3, using
(103, 103+14, 238810)-Net over F3 — Digital
Digital (103, 117, 238810)-net over F3, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3117, 238810, F3, 2, 14) (dual of [(238810, 2), 477503, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3117, 265742, F3, 2, 14) (dual of [(265742, 2), 531367, 15]-NRT-code), using
- 31 times duplication [i] based on linear OOA(3116, 265742, F3, 2, 14) (dual of [(265742, 2), 531368, 15]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3116, 531484, F3, 14) (dual of [531484, 531368, 15]-code), using
- 1 times code embedding in larger space [i] based on linear OA(3115, 531483, F3, 14) (dual of [531483, 531368, 15]-code), using
- construction X applied to Ce(13) ⊂ Ce(9) [i] based on
- linear OA(3109, 531441, F3, 14) (dual of [531441, 531332, 15]-code), using an extension Ce(13) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 14 [i]
- linear OA(373, 531441, F3, 10) (dual of [531441, 531368, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 531440 = 312−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(36, 42, F3, 3) (dual of [42, 36, 4]-code or 42-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(13) ⊂ Ce(9) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(3115, 531483, F3, 14) (dual of [531483, 531368, 15]-code), using
- OOA 2-folding [i] based on linear OA(3116, 531484, F3, 14) (dual of [531484, 531368, 15]-code), using
- 31 times duplication [i] based on linear OOA(3116, 265742, F3, 2, 14) (dual of [(265742, 2), 531368, 15]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3117, 265742, F3, 2, 14) (dual of [(265742, 2), 531367, 15]-NRT-code), using
(103, 103+14, large)-Net in Base 3 — Upper bound on s
There is no (103, 117, large)-net in base 3, because
- 12 times m-reduction [i] would yield (103, 105, large)-net in base 3, but