Best Known (115−25, 115, s)-Nets in Base 16
(115−25, 115, 10971)-Net over F16 — Constructive and digital
Digital (90, 115, 10971)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (5, 17, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- digital (73, 98, 10922)-net over F16, using
- net defined by OOA [i] based on linear OOA(1698, 10922, F16, 25, 25) (dual of [(10922, 25), 272952, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(1698, 131065, F16, 25) (dual of [131065, 130967, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 131074, F16, 25) (dual of [131074, 130976, 26]-code), using
- trace code [i] based on linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 65537 | 2564−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- trace code [i] based on linear OA(25649, 65537, F256, 25) (dual of [65537, 65488, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(1698, 131074, F16, 25) (dual of [131074, 130976, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(1698, 131065, F16, 25) (dual of [131065, 130967, 26]-code), using
- net defined by OOA [i] based on linear OOA(1698, 10922, F16, 25, 25) (dual of [(10922, 25), 272952, 26]-NRT-code), using
- digital (5, 17, 49)-net over F16, using
(115−25, 115, 21846)-Net in Base 16 — Constructive
(90, 115, 21846)-net in base 16, using
- 161 times duplication [i] based on (89, 114, 21846)-net in base 16, using
- base change [i] based on digital (51, 76, 21846)-net over F64, using
- 641 times duplication [i] based on digital (50, 75, 21846)-net over F64, using
- net defined by OOA [i] based on linear OOA(6475, 21846, F64, 25, 25) (dual of [(21846, 25), 546075, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6475, 262153, F64, 25) (dual of [262153, 262078, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(6475, 262155, F64, 25) (dual of [262155, 262080, 26]-code), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- linear OA(6473, 262144, F64, 25) (dual of [262144, 262071, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(6464, 262144, F64, 22) (dual of [262144, 262080, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 262143 = 643−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(642, 11, F64, 2) (dual of [11, 9, 3]-code or 11-arc in PG(1,64)), using
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- Reed–Solomon code RS(62,64) [i]
- discarding factors / shortening the dual code based on linear OA(642, 64, F64, 2) (dual of [64, 62, 3]-code or 64-arc in PG(1,64)), using
- construction X applied to Ce(24) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(6475, 262155, F64, 25) (dual of [262155, 262080, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(6475, 262153, F64, 25) (dual of [262153, 262078, 26]-code), using
- net defined by OOA [i] based on linear OOA(6475, 21846, F64, 25, 25) (dual of [(21846, 25), 546075, 26]-NRT-code), using
- 641 times duplication [i] based on digital (50, 75, 21846)-net over F64, using
- base change [i] based on digital (51, 76, 21846)-net over F64, using
(115−25, 115, 384615)-Net over F16 — Digital
Digital (90, 115, 384615)-net over F16, using
(115−25, 115, large)-Net in Base 16 — Upper bound on s
There is no (90, 115, large)-net in base 16, because
- 23 times m-reduction [i] would yield (90, 92, large)-net in base 16, but