Best Known (46−16, 46, s)-Nets in Base 49
(46−16, 46, 14706)-Net over F49 — Constructive and digital
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
(46−16, 46, 58826)-Net over F49 — Digital
Digital (30, 46, 58826)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4946, 58826, F49, 2, 16) (dual of [(58826, 2), 117606, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(4946, 117652, F49, 16) (dual of [117652, 117606, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] 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]
- linear OA(4943, 117649, F49, 15) (dual of [117649, 117606, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 493−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(490, 3, F49, 0) (dual of [3, 3, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- OOA 2-folding [i] based on linear OA(4946, 117652, F49, 16) (dual of [117652, 117606, 17]-code), using
(46−16, 46, large)-Net in Base 49 — Upper bound on s
There is no (30, 46, large)-net in base 49, because
- 14 times m-reduction [i] would yield (30, 32, large)-net in base 49, but