Best Known (54, 54+22, s)-Nets in Base 128
(54, 54+22, 190800)-Net over F128 — Constructive and digital
Digital (54, 76, 190800)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (1, 12, 150)-net over F128, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 1 and N(F) ≥ 150, using
- net from sequence [i] based on digital (1, 149)-sequence over F128, using
- digital (42, 64, 190650)-net over F128, using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- discarding factors / shortening the dual code based on linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using
- an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(12864, 2097152, F128, 22) (dual of [2097152, 2097088, 23]-code), using
- OA 11-folding and stacking [i] based on linear OA(12864, 2097150, F128, 22) (dual of [2097150, 2097086, 23]-code), using
- net defined by OOA [i] based on linear OOA(12864, 190650, F128, 22, 22) (dual of [(190650, 22), 4194236, 23]-NRT-code), using
- digital (1, 12, 150)-net over F128, using
(54, 54+22, 762600)-Net in Base 128 — Constructive
(54, 76, 762600)-net in base 128, using
- 1 times m-reduction [i] based on (54, 77, 762600)-net in base 128, using
- net defined by OOA [i] based on OOA(12877, 762600, S128, 23, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(12877, 8388601, S128, 23), using
- discarding factors based on OA(12877, large, S128, 23), using
- discarding parts of the base [i] based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,22], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding parts of the base [i] based on linear OA(25667, large, F256, 23) (dual of [large, large−67, 24]-code), using
- discarding factors based on OA(12877, large, S128, 23), using
- OOA 11-folding and stacking with additional row [i] based on OA(12877, 8388601, S128, 23), using
- net defined by OOA [i] based on OOA(12877, 762600, S128, 23, 23), using
(54, 54+22, 2889240)-Net over F128 — Digital
Digital (54, 76, 2889240)-net over F128, using
(54, 54+22, large)-Net in Base 128 — Upper bound on s
There is no (54, 76, large)-net in base 128, because
- 20 times m-reduction [i] would yield (54, 56, large)-net in base 128, but