Best Known (40, 50, s)-Nets in Base 16
(40, 50, 209720)-Net over F16 — Constructive and digital
Digital (40, 50, 209720)-net over F16, using
- net defined by OOA [i] based on linear OOA(1650, 209720, F16, 10, 10) (dual of [(209720, 10), 2097150, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(1650, 1048600, F16, 10) (dual of [1048600, 1048550, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- linear OA(1646, 1048576, F16, 10) (dual of [1048576, 1048530, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(1626, 1048576, F16, 6) (dual of [1048576, 1048550, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- linear OA(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- OA 5-folding and stacking [i] based on linear OA(1650, 1048600, F16, 10) (dual of [1048600, 1048550, 11]-code), using
(40, 50, 419431)-Net in Base 16 — Constructive
(40, 50, 419431)-net in base 16, using
- 161 times duplication [i] based on (39, 49, 419431)-net in base 16, using
- base change [i] based on digital (18, 28, 419431)-net over F128, using
- net defined by OOA [i] based on linear OOA(12828, 419431, F128, 10, 10) (dual of [(419431, 10), 4194282, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(12828, 2097155, F128, 10) (dual of [2097155, 2097127, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(8) [i] based on
- 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(12825, 2097152, F128, 9) (dual of [2097152, 2097127, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 2097151 = 1283−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [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(9) ⊂ Ce(8) [i] based on
- OA 5-folding and stacking [i] based on linear OA(12828, 2097155, F128, 10) (dual of [2097155, 2097127, 11]-code), using
- net defined by OOA [i] based on linear OOA(12828, 419431, F128, 10, 10) (dual of [(419431, 10), 4194282, 11]-NRT-code), using
- base change [i] based on digital (18, 28, 419431)-net over F128, using
(40, 50, 1352749)-Net over F16 — Digital
Digital (40, 50, 1352749)-net over F16, using
(40, 50, large)-Net in Base 16 — Upper bound on s
There is no (40, 50, large)-net in base 16, because
- 8 times m-reduction [i] would yield (40, 42, large)-net in base 16, but