Best Known (25, 25+9, s)-Nets in Base 128
(25, 25+9, 2097150)-Net over F128 — Constructive and digital
Digital (25, 34, 2097150)-net over F128, using
- 1281 times duplication [i] based on digital (24, 33, 2097150)-net over F128, using
- net defined by OOA [i] based on linear OOA(12833, 2097150, F128, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(12833, 8388601, F128, 9) (dual of [8388601, 8388568, 10]-code), using
- discarding factors / shortening the dual code based on linear OA(12833, large, F128, 9) (dual of [large, large−33, 10]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 15790321 | 1288−1, defining interval I = [0,4], and minimum distance d ≥ |{−4,−3,…,4}|+1 = 10 (BCH-bound) [i]
- discarding factors / shortening the dual code based on linear OA(12833, large, F128, 9) (dual of [large, large−33, 10]-code), using
- OOA 4-folding and stacking with additional row [i] based on linear OA(12833, 8388601, F128, 9) (dual of [8388601, 8388568, 10]-code), using
- net defined by OOA [i] based on linear OOA(12833, 2097150, F128, 9, 9) (dual of [(2097150, 9), 18874317, 10]-NRT-code), using
(25, 25+9, 2097407)-Net in Base 128 — Constructive
(25, 34, 2097407)-net in base 128, using
- (u, u+v)-construction [i] based on
- (1, 5, 257)-net in base 128, using
- 3 times m-reduction [i] based on (1, 8, 257)-net in base 128, using
- base change [i] based on digital (0, 7, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- base change [i] based on digital (0, 7, 257)-net over F256, using
- 3 times m-reduction [i] based on (1, 8, 257)-net in base 128, using
- (20, 29, 2097150)-net in base 128, using
- net defined by OOA [i] based on OOA(12829, 2097150, S128, 9, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(12829, 8388601, S128, 9), using
- discarding factors based on OA(12829, large, S128, 9), using
- discarding parts of the base [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,8], and designed minimum distance d ≥ |I|+1 = 10 [i]
- discarding parts of the base [i] based on linear OA(25625, large, F256, 9) (dual of [large, large−25, 10]-code), using
- discarding factors based on OA(12829, large, S128, 9), using
- OOA 4-folding and stacking with additional row [i] based on OA(12829, 8388601, S128, 9), using
- net defined by OOA [i] based on OOA(12829, 2097150, S128, 9, 9), using
- (1, 5, 257)-net in base 128, using
(25, 25+9, large)-Net over F128 — Digital
Digital (25, 34, large)-net over F128, using
- 1281 times duplication [i] based on digital (24, 33, large)-net over F128, using
(25, 25+9, large)-Net in Base 128 — Upper bound on s
There is no (25, 34, large)-net in base 128, because
- 7 times m-reduction [i] would yield (25, 27, large)-net in base 128, but