Best Known (39, 39+16, s)-Nets in Base 49
(39, 39+16, 14757)-Net over F49 — Constructive and digital
Digital (39, 55, 14757)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (30, 46, 14706)-net over F49, using
- net defined by OOA [i] based on linear OOA(4946, 14706, F49, 16, 16) (dual of [(14706, 16), 235250, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(4946, 117648, F49, 16) (dual of [117648, 117602, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(4946, 117649, F49, 16) (dual of [117649, 117603, 17]-code), using
- an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- discarding factors / shortening the dual code based on linear OA(4946, 117649, F49, 16) (dual of [117649, 117603, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(4946, 117648, F49, 16) (dual of [117648, 117602, 17]-code), using
- net defined by OOA [i] based on linear OOA(4946, 14706, F49, 16, 16) (dual of [(14706, 16), 235250, 17]-NRT-code), using
- digital (1, 9, 51)-net over F49, using
(39, 39+16, 210827)-Net over F49 — Digital
Digital (39, 55, 210827)-net over F49, using
(39, 39+16, large)-Net in Base 49 — Upper bound on s
There is no (39, 55, large)-net in base 49, because
- 14 times m-reduction [i] would yield (39, 41, large)-net in base 49, but