Best Known (39−5, 39, s)-Nets in Base 128
(39−5, 39, large)-Net over F128 — Constructive and digital
Digital (34, 39, large)-net over F128, using
- 1281 times duplication [i] based on digital (33, 38, large)-net over F128, using
- t-expansion [i] based on digital (31, 38, 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 (24, 31, 4926250)-net over F128, using
- net defined by OOA [i] based on linear OOA(12831, 4926250, F128, 9, 7) (dual of [(4926250, 9), 44336219, 8]-NRT-code), using
- OOA stacking with additional row [i] based on linear OOA(12831, 4926251, F128, 3, 7) (dual of [(4926251, 3), 14778722, 8]-NRT-code), using
- (u, u+v)-construction [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
- linear OOA(12825, 2796201, F128, 3, 7) (dual of [(2796201, 3), 8388578, 8]-NRT-code), using
- OOA 3-folding [i] based on linear OA(12825, large, F128, 7) (dual of [large, large−25, 8]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 17895697 | 1284−1, defining interval I = [0,6], and designed minimum distance d ≥ |I|+1 = 8 [i]
- OOA 3-folding [i] based on linear OA(12825, large, F128, 7) (dual of [large, large−25, 8]-code), using
- linear OOA(1286, 2130050, F128, 3, 3) (dual of [(2130050, 3), 6390144, 4]-NRT-code), using
- (u, u+v)-construction [i] based on
- OOA stacking with additional row [i] based on linear OOA(12831, 4926251, F128, 3, 7) (dual of [(4926251, 3), 14778722, 8]-NRT-code), using
- net defined by OOA [i] based on linear OOA(12831, 4926250, F128, 9, 7) (dual of [(4926250, 9), 44336219, 8]-NRT-code), using
- digital (4, 7, large)-net over F128, using
- (u, u+v)-construction [i] based on
- t-expansion [i] based on digital (31, 38, large)-net over F128, using
(39−5, 39, large)-Net in Base 128 — Upper bound on s
There is no (34, 39, large)-net in base 128, because
- 3 times m-reduction [i] would yield (34, 36, large)-net in base 128, but