Best Known (46, 62, s)-Nets in Base 9
(46, 62, 1640)-Net over F9 — Constructive and digital
Digital (46, 62, 1640)-net over F9, using
- net defined by OOA [i] based on linear OOA(962, 1640, F9, 16, 16) (dual of [(1640, 16), 26178, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(962, 13120, F9, 16) (dual of [13120, 13058, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(962, 13122, F9, 16) (dual of [13122, 13060, 17]-code), using
- trace code [i] based on linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- trace code [i] based on linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(962, 13122, F9, 16) (dual of [13122, 13060, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(962, 13120, F9, 16) (dual of [13120, 13058, 17]-code), using
(46, 62, 10860)-Net over F9 — Digital
Digital (46, 62, 10860)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(962, 10860, F9, 16) (dual of [10860, 10798, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(962, 13122, F9, 16) (dual of [13122, 13060, 17]-code), using
- trace code [i] based on linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 6560 = 812−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- trace code [i] based on linear OA(8131, 6561, F81, 16) (dual of [6561, 6530, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(962, 13122, F9, 16) (dual of [13122, 13060, 17]-code), using
(46, 62, large)-Net in Base 9 — Upper bound on s
There is no (46, 62, large)-net in base 9, because
- 14 times m-reduction [i] would yield (46, 48, large)-net in base 9, but