Best Known (120−10, 120, s)-Nets in Base 3
(120−10, 120, 1913194)-Net over F3 — Constructive and digital
Digital (110, 120, 1913194)-net over F3, using
- trace code for nets [i] based on digital (50, 60, 956597)-net over F9, using
- net defined by OOA [i] based on linear OOA(960, 956597, F9, 10, 10) (dual of [(956597, 10), 9565910, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(960, 4782985, F9, 10) (dual of [4782985, 4782925, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(960, 4782986, F9, 10) (dual of [4782986, 4782926, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(943, 4782969, F9, 7) (dual of [4782969, 4782926, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(93, 17, F9, 2) (dual of [17, 14, 3]-code), using
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 80 = 92−1, defining interval I = [0,1], and designed minimum distance d ≥ |I|+1 = 3 [i]
- discarding factors / shortening the dual code based on linear OA(93, 80, F9, 2) (dual of [80, 77, 3]-code), using
- construction X applied to Ce(9) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(960, 4782986, F9, 10) (dual of [4782986, 4782926, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(960, 4782985, F9, 10) (dual of [4782985, 4782925, 11]-code), using
- net defined by OOA [i] based on linear OOA(960, 956597, F9, 10, 10) (dual of [(956597, 10), 9565910, 11]-NRT-code), using
(120−10, 120, large)-Net over F3 — Digital
Digital (110, 120, large)-net over F3, using
- 37 times duplication [i] based on digital (103, 113, large)-net over F3, using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3113, large, F3, 10) (dual of [large, large−113, 11]-code), using
- 22 times code embedding in larger space [i] based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 14348906 = 315−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [i]
- 22 times code embedding in larger space [i] based on linear OA(391, large, F3, 10) (dual of [large, large−91, 11]-code), using
- embedding of OOA with Gilbert–VarÅ¡amov bound [i] based on linear OA(3113, large, F3, 10) (dual of [large, large−113, 11]-code), using
(120−10, 120, large)-Net in Base 3 — Upper bound on s
There is no (110, 120, large)-net in base 3, because
- 8 times m-reduction [i] would yield (110, 112, large)-net in base 3, but