Best Known (80, 80+20, s)-Nets in Base 16
(80, 80+20, 104861)-Net over F16 — Constructive and digital
Digital (80, 100, 104861)-net over F16, using
- net defined by OOA [i] based on linear OOA(16100, 104861, F16, 20, 20) (dual of [(104861, 20), 2097120, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(16100, 1048610, F16, 20) (dual of [1048610, 1048510, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(16100, 1048614, F16, 20) (dual of [1048614, 1048514, 21]-code), using
- construction X applied to Ce(19) ⊂ Ce(12) [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(1661, 1048576, F16, 13) (dual of [1048576, 1048515, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(169, 38, F16, 6) (dual of [38, 29, 7]-code), using
- extended algebraic-geometric code AGe(F,31P) [i] based on function field F/F16 with g(F) = 3 and N(F) ≥ 38, using
- construction X applied to Ce(19) ⊂ Ce(12) [i] based on
- discarding factors / shortening the dual code based on linear OA(16100, 1048614, F16, 20) (dual of [1048614, 1048514, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(16100, 1048610, F16, 20) (dual of [1048610, 1048510, 21]-code), using
(80, 80+20, 1149745)-Net over F16 — Digital
Digital (80, 100, 1149745)-net over F16, using
(80, 80+20, large)-Net in Base 16 — Upper bound on s
There is no (80, 100, large)-net in base 16, because
- 18 times m-reduction [i] would yield (80, 82, large)-net in base 16, but