Best Known (31−3, 31, s)-Nets in Base 128
(31−3, 31, large)-Net over F128 — Constructive and digital
Digital (28, 31, large)-net over F128, using
- 3 times m-reduction [i] based on digital (28, 34, large)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (4, 7, large)-net over F128, using
- net defined by OOA [i] based on linear OOA(1287, large, F128, 3, 3), using
- appending kth column [i] based on linear OOA(1287, large, F128, 2, 3), using
- OAs with strength 3, b ≠ 2, and m > 3 are always embeddable [i] based on linear OA(1287, large, F128, 3) (dual of [large, large−7, 4]-code), using
- appending kth column [i] based on linear OOA(1287, large, F128, 2, 3), using
- net defined by OOA [i] based on linear OOA(1287, large, F128, 3, 3), using
- digital (21, 27, 4926251)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (3, 6, 2130050)-net over F128, using
- net defined by OOA [i] based on linear OOA(1286, 2130050, F128, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(1286, 2130050, F128, 2, 3) (dual of [(2130050, 2), 4260094, 4]-NRT-code), using
- net defined by OOA [i] based on linear OOA(1286, 2130050, F128, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
- digital (15, 21, 2796201)-net over F128, using
- net defined by OOA [i] based on linear OOA(12821, 2796201, F128, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,5], and designed minimum distance d ≥ |I|+1 = 7 [i]
- OA 3-folding and stacking [i] based on linear OA(12821, large, F128, 6) (dual of [large, large−21, 7]-code), using
- net defined by OOA [i] based on linear OOA(12821, 2796201, F128, 6, 6) (dual of [(2796201, 6), 16777185, 7]-NRT-code), using
- digital (3, 6, 2130050)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (4, 7, large)-net over F128, using
- (u, u+v)-construction [i] based on
(31−3, 31, large)-Net in Base 128 — Upper bound on s
There is no (28, 31, large)-net in base 128, because
- 1 times m-reduction [i] would yield (28, 30, large)-net in base 128, but