Best Known (64, 64+16, s)-Nets in Base 16
(64, 64+16, 131075)-Net over F16 — Constructive and digital
Digital (64, 80, 131075)-net over F16, using
- net defined by OOA [i] based on linear OOA(1680, 131075, F16, 16, 16) (dual of [(131075, 16), 2097120, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(1680, 1048600, F16, 16) (dual of [1048600, 1048520, 17]-code), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- linear OA(1676, 1048576, F16, 17) (dual of [1048576, 1048500, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(1656, 1048576, F16, 12) (dual of [1048576, 1048520, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 1048575 = 165−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(164, 24, F16, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,16)), using
- construction X applied to Ce(16) ⊂ Ce(11) [i] based on
- OA 8-folding and stacking [i] based on linear OA(1680, 1048600, F16, 16) (dual of [1048600, 1048520, 17]-code), using
(64, 64+16, 1131492)-Net over F16 — Digital
Digital (64, 80, 1131492)-net over F16, using
(64, 64+16, large)-Net in Base 16 — Upper bound on s
There is no (64, 80, large)-net in base 16, because
- 14 times m-reduction [i] would yield (64, 66, large)-net in base 16, but