Best Known (25, 25+11, s)-Nets in Base 128
(25, 25+11, 419559)-Net over F128 — Constructive and digital
Digital (25, 36, 419559)-net over F128, using
- (u, u+v)-construction [i] based on
- digital (0, 5, 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 (20, 31, 419430)-net over F128, using
- net defined by OOA [i] based on linear OOA(12831, 419430, F128, 11, 11) (dual of [(419430, 11), 4613699, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12831, 2097151, F128, 11) (dual of [2097151, 2097120, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using
- an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- discarding factors / shortening the dual code based on linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(12831, 2097151, F128, 11) (dual of [2097151, 2097120, 12]-code), using
- net defined by OOA [i] based on linear OOA(12831, 419430, F128, 11, 11) (dual of [(419430, 11), 4613699, 12]-NRT-code), using
- digital (0, 5, 129)-net over F128, using
(25, 25+11, 1677720)-Net in Base 128 — Constructive
(25, 36, 1677720)-net in base 128, using
- net defined by OOA [i] based on OOA(12836, 1677720, S128, 11, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(12836, 8388601, S128, 11), using
- discarding factors based on OA(12836, large, S128, 11), using
- discarding parts of the base [i] based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 16777215 = 2563−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- discarding parts of the base [i] based on linear OA(25631, large, F256, 11) (dual of [large, large−31, 12]-code), using
- discarding factors based on OA(12836, large, S128, 11), using
- OOA 5-folding and stacking with additional row [i] based on OA(12836, 8388601, S128, 11), using
(25, 25+11, 2097284)-Net over F128 — Digital
Digital (25, 36, 2097284)-net over F128, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(12836, 2097284, F128, 11) (dual of [2097284, 2097248, 12]-code), using
- (u, u+v)-construction [i] based on
- linear OA(1285, 129, F128, 5) (dual of [129, 124, 6]-code or 129-arc in PG(4,128)), using
- extended Reed–Solomon code RSe(124,128) [i]
- linear OA(12831, 2097155, F128, 11) (dual of [2097155, 2097124, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(12831, 2097152, F128, 11) (dual of [2097152, 2097121, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(12828, 2097152, F128, 10) (dual of [2097152, 2097124, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1280, 3, F128, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(1280, s, F128, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(10) ⊂ Ce(9) [i] based on
- linear OA(1285, 129, F128, 5) (dual of [129, 124, 6]-code or 129-arc in PG(4,128)), using
- (u, u+v)-construction [i] based on
(25, 25+11, large)-Net in Base 128 — Upper bound on s
There is no (25, 36, large)-net in base 128, because
- 9 times m-reduction [i] would yield (25, 27, large)-net in base 128, but