Best Known (99, 99+24, s)-Nets in Base 16
(99, 99+24, 87398)-Net over F16 — Constructive and digital
Digital (99, 123, 87398)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (0, 12, 17)-net over F16, using
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 0 and N(F) ≥ 17, using
- the rational function field F16(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 16)-sequence over F16, using
- digital (87, 111, 87381)-net over F16, using
- net defined by OOA [i] based on linear OOA(16111, 87381, F16, 24, 24) (dual of [(87381, 24), 2097033, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(16111, 1048572, F16, 24) (dual of [1048572, 1048461, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(16111, 1048576, F16, 24) (dual of [1048576, 1048465, 25]-code), using
- an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- discarding factors / shortening the dual code based on linear OA(16111, 1048576, F16, 24) (dual of [1048576, 1048465, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(16111, 1048572, F16, 24) (dual of [1048572, 1048461, 25]-code), using
- net defined by OOA [i] based on linear OOA(16111, 87381, F16, 24, 24) (dual of [(87381, 24), 2097033, 25]-NRT-code), using
- digital (0, 12, 17)-net over F16, using
(99, 99+24, 174762)-Net in Base 16 — Constructive
(99, 123, 174762)-net in base 16, using
- net defined by OOA [i] based on OOA(16123, 174762, S16, 24, 24), using
- OA 12-folding and stacking [i] based on OA(16123, 2097144, S16, 24), using
- discarding factors based on OA(16123, 2097155, S16, 24), using
- discarding parts of the base [i] based on linear OA(12870, 2097155, F128, 24) (dual of [2097155, 2097085, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(12870, 2097152, F128, 24) (dual of [2097152, 2097082, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- 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]
- 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(23) ⊂ Ce(22) [i] based on
- discarding parts of the base [i] based on linear OA(12870, 2097155, F128, 24) (dual of [2097155, 2097085, 25]-code), using
- discarding factors based on OA(16123, 2097155, S16, 24), using
- OA 12-folding and stacking [i] based on OA(16123, 2097144, S16, 24), using
(99, 99+24, 1728989)-Net over F16 — Digital
Digital (99, 123, 1728989)-net over F16, using
(99, 99+24, large)-Net in Base 16 — Upper bound on s
There is no (99, 123, large)-net in base 16, because
- 22 times m-reduction [i] would yield (99, 101, large)-net in base 16, but