Best Known (127−10, 127, s)-Nets in Base 3
(127−10, 127, 1913289)-Net over F3 — Constructive and digital
Digital (117, 127, 1913289)-net over F3, using
- (u, u+v)-construction [i] based on
- digital (8, 13, 103)-net over F3, using
- digital (104, 114, 1913186)-net over F3, using
- trace code for nets [i] based on digital (47, 57, 956593)-net over F9, using
- net defined by OOA [i] based on linear OOA(957, 956593, F9, 10, 10) (dual of [(956593, 10), 9565873, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(957, 4782965, F9, 10) (dual of [4782965, 4782908, 11]-code), using
- discarding factors / shortening the dual code 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]
- discarding factors / shortening the dual code based on linear OA(957, 4782969, F9, 10) (dual of [4782969, 4782912, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(957, 4782965, F9, 10) (dual of [4782965, 4782908, 11]-code), using
- net defined by OOA [i] based on linear OOA(957, 956593, F9, 10, 10) (dual of [(956593, 10), 9565873, 11]-NRT-code), using
- trace code for nets [i] based on digital (47, 57, 956593)-net over F9, using
(127−10, 127, large)-Net over F3 — Digital
Digital (117, 127, large)-net over F3, using
- 31 times duplication [i] based on digital (116, 126, large)-net over F3, using
- t-expansion [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
- t-expansion [i] based on digital (115, 126, large)-net over F3, using
(127−10, 127, large)-Net in Base 3 — Upper bound on s
There is no (117, 127, large)-net in base 3, because
- 8 times m-reduction [i] would yield (117, 119, large)-net in base 3, but