Best Known (79, 108, s)-Nets in Base 16
(79, 108, 1546)-Net over F16 — Constructive and digital
Digital (79, 108, 1546)-net over F16, using
- generalized (u, u+v)-construction [i] based on
- digital (9, 18, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 9, 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
- trace code for nets [i] based on digital (0, 9, 257)-net over F256, using
- digital (16, 30, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 15, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256, using
- trace code for nets [i] based on digital (1, 15, 258)-net over F256, using
- digital (31, 60, 516)-net over F16, using
- trace code for nets [i] based on digital (1, 30, 258)-net over F256, using
- net from sequence [i] based on digital (1, 257)-sequence over F256 (see above)
- trace code for nets [i] based on digital (1, 30, 258)-net over F256, using
- digital (9, 18, 514)-net over F16, using
(79, 108, 2341)-Net in Base 16 — Constructive
(79, 108, 2341)-net in base 16, using
- net defined by OOA [i] based on OOA(16108, 2341, S16, 29, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(16108, 32775, S16, 29), using
- discarding factors based on OA(16108, 32776, S16, 29), using
- discarding parts of the base [i] based on linear OA(3286, 32776, F32, 29) (dual of [32776, 32690, 30]-code), using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- linear OA(3285, 32769, F32, 29) (dual of [32769, 32684, 30]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,14], and minimum distance d ≥ |{−14,−13,…,14}|+1 = 30 (BCH-bound) [i]
- linear OA(3279, 32769, F32, 27) (dual of [32769, 32690, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 32769 | 326−1, defining interval I = [0,13], and minimum distance d ≥ |{−13,−12,…,13}|+1 = 28 (BCH-bound) [i]
- linear OA(321, 7, F32, 1) (dual of [7, 6, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,14]) ⊂ C([0,13]) [i] based on
- discarding parts of the base [i] based on linear OA(3286, 32776, F32, 29) (dual of [32776, 32690, 30]-code), using
- discarding factors based on OA(16108, 32776, S16, 29), using
- OOA 14-folding and stacking with additional row [i] based on OA(16108, 32775, S16, 29), using
(79, 108, 33232)-Net over F16 — Digital
Digital (79, 108, 33232)-net over F16, using
(79, 108, large)-Net in Base 16 — Upper bound on s
There is no (79, 108, large)-net in base 16, because
- 27 times m-reduction [i] would yield (79, 81, large)-net in base 16, but