Best Known (99, 99+31, s)-Nets in Base 16
(99, 99+31, 8739)-Net over F16 — Constructive and digital
Digital (99, 130, 8739)-net over F16, using
- 164 times duplication [i] based on digital (95, 126, 8739)-net over F16, using
- net defined by OOA [i] based on linear OOA(16126, 8739, F16, 31, 31) (dual of [(8739, 31), 270783, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16126, 131086, F16, 31) (dual of [131086, 130960, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16126, 131088, F16, 31) (dual of [131088, 130962, 32]-code), using
- trace code [i] based on linear OA(25663, 65544, F256, 31) (dual of [65544, 65481, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- linear OA(25661, 65536, F256, 31) (dual of [65536, 65475, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(25655, 65536, F256, 28) (dual of [65536, 65481, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 2562−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(2562, 8, F256, 2) (dual of [8, 6, 3]-code or 8-arc in PG(1,256)), using
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- Reed–Solomon code RS(254,256) [i]
- discarding factors / shortening the dual code based on linear OA(2562, 256, F256, 2) (dual of [256, 254, 3]-code or 256-arc in PG(1,256)), using
- construction X applied to Ce(30) ⊂ Ce(27) [i] based on
- trace code [i] based on linear OA(25663, 65544, F256, 31) (dual of [65544, 65481, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(16126, 131088, F16, 31) (dual of [131088, 130962, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(16126, 131086, F16, 31) (dual of [131086, 130960, 32]-code), using
- net defined by OOA [i] based on linear OOA(16126, 8739, F16, 31, 31) (dual of [(8739, 31), 270783, 32]-NRT-code), using
(99, 99+31, 132617)-Net over F16 — Digital
Digital (99, 130, 132617)-net over F16, using
(99, 99+31, large)-Net in Base 16 — Upper bound on s
There is no (99, 130, large)-net in base 16, because
- 29 times m-reduction [i] would yield (99, 101, large)-net in base 16, but