Best Known (78−23, 78, s)-Nets in Base 128
(78−23, 78, 190779)-Net over F128 — Constructive and digital
Digital (55, 78, 190779)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 11, 129)-net over F128, using
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 0 and N(F) ≥ 129, using
- the rational function field F128(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 128)-sequence over F128, using
- digital (44, 67, 190650)-net over F128, using
- net defined by OOA [i] based on linear OOA(12867, 190650, F128, 23, 23) (dual of [(190650, 23), 4384883, 24]-NRT-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12867, 2097151, F128, 23) (dual of [2097151, 2097084, 24]-code), using
- discarding factors / shortening the dual code based on linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using
- an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- discarding factors / shortening the dual code based on linear OA(12867, 2097152, F128, 23) (dual of [2097152, 2097085, 24]-code), using
- OOA 11-folding and stacking with additional row [i] based on linear OA(12867, 2097151, F128, 23) (dual of [2097151, 2097084, 24]-code), using
- net defined by OOA [i] based on linear OOA(12867, 190650, F128, 23, 23) (dual of [(190650, 23), 4384883, 24]-NRT-code), using
- digital (0, 11, 129)-net over F128, using
(78−23, 78, 762600)-Net in Base 128 — Constructive
(55, 78, 762600)-net in base 128, using
- 1281 times duplication [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
(78−23, 78, 2108962)-Net over F128 — Digital
Digital (55, 78, 2108962)-net over F128, using
(78−23, 78, large)-Net in Base 128 — Upper bound on s
There is no (55, 78, large)-net in base 128, because
- 21 times m-reduction [i] would yield (55, 57, large)-net in base 128, but