Best Known (79, 107, s)-Nets in Base 16
(79, 107, 4682)-Net over F16 — Constructive and digital
Digital (79, 107, 4682)-net over F16, using
- net defined by OOA [i] based on linear OOA(16107, 4682, F16, 28, 28) (dual of [(4682, 28), 130989, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(16107, 65548, F16, 28) (dual of [65548, 65441, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(16107, 65548, F16, 28) (dual of [65548, 65441, 29]-code), using
(79, 107, 57043)-Net over F16 — Digital
Digital (79, 107, 57043)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16107, 57043, F16, 28) (dual of [57043, 56936, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- linear OA(16105, 65536, F16, 28) (dual of [65536, 65431, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(1693, 65536, F16, 25) (dual of [65536, 65443, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(162, 14, F16, 2) (dual of [14, 12, 3]-code or 14-arc in PG(1,16)), using
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- Reed–Solomon code RS(14,16) [i]
- discarding factors / shortening the dual code based on linear OA(162, 16, F16, 2) (dual of [16, 14, 3]-code or 16-arc in PG(1,16)), using
- construction X applied to Ce(27) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(16107, 65550, F16, 28) (dual of [65550, 65443, 29]-code), using
(79, 107, large)-Net in Base 16 — Upper bound on s
There is no (79, 107, large)-net in base 16, because
- 26 times m-reduction [i] would yield (79, 81, large)-net in base 16, but