Best Known (75, 102, s)-Nets in Base 16
(75, 102, 5041)-Net over F16 — Constructive and digital
Digital (75, 102, 5041)-net over F16, using
- 161 times duplication [i] based on digital (74, 101, 5041)-net over F16, using
- net defined by OOA [i] based on linear OOA(16101, 5041, F16, 27, 27) (dual of [(5041, 27), 136006, 28]-NRT-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16101, 65534, F16, 27) (dual of [65534, 65433, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using
- an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- discarding factors / shortening the dual code based on linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using
- OOA 13-folding and stacking with additional row [i] based on linear OA(16101, 65534, F16, 27) (dual of [65534, 65433, 28]-code), using
- net defined by OOA [i] based on linear OOA(16101, 5041, F16, 27, 27) (dual of [(5041, 27), 136006, 28]-NRT-code), using
(75, 102, 49667)-Net over F16 — Digital
Digital (75, 102, 49667)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16102, 49667, F16, 27) (dual of [49667, 49565, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(16102, 65545, F16, 27) (dual of [65545, 65443, 28]-code), using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- linear OA(16101, 65536, F16, 27) (dual of [65536, 65435, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 65535 = 164−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [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(161, 9, F16, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(161, s, F16, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(26) ⊂ Ce(24) [i] based on
- discarding factors / shortening the dual code based on linear OA(16102, 65545, F16, 27) (dual of [65545, 65443, 28]-code), using
(75, 102, large)-Net in Base 16 — Upper bound on s
There is no (75, 102, large)-net in base 16, because
- 25 times m-reduction [i] would yield (75, 77, large)-net in base 16, but