Best Known (91−20, 91, s)-Nets in Base 16
(91−20, 91, 104858)-Net over F16 — Constructive and digital
Digital (71, 91, 104858)-net over F16, using
- net defined by OOA [i] based on linear OOA(1691, 104858, F16, 20, 20) (dual of [(104858, 20), 2097069, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(1691, 1048580, F16, 20) (dual of [1048580, 1048489, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1691, 1048581, F16, 20) (dual of [1048581, 1048490, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- linear OA(1686, 1048576, F16, 19) (dual of [1048576, 1048490, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(160, 5, F16, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(160, s, F16, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(19) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(1691, 1048581, F16, 20) (dual of [1048581, 1048490, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(1691, 1048580, F16, 20) (dual of [1048580, 1048489, 21]-code), using
(91−20, 91, 527997)-Net over F16 — Digital
Digital (71, 91, 527997)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(1691, 527997, F16, 20) (dual of [527997, 527906, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using
- an extension Ce(19) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,19], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(1691, 1048576, F16, 20) (dual of [1048576, 1048485, 21]-code), using
(91−20, 91, large)-Net in Base 16 — Upper bound on s
There is no (71, 91, large)-net in base 16, because
- 18 times m-reduction [i] would yield (71, 73, large)-net in base 16, but