Best Known (64, 64+16, s)-Nets in Base 7
(64, 64+16, 14707)-Net over F7 — Constructive and digital
Digital (64, 80, 14707)-net over F7, using
- net defined by OOA [i] based on linear OOA(780, 14707, F7, 16, 16) (dual of [(14707, 16), 235232, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(780, 117656, F7, 16) (dual of [117656, 117576, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(779, 117655, F7, 16) (dual of [117655, 117576, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(70, 6, F7, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(779, 117655, F7, 16) (dual of [117655, 117576, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(780, 117656, F7, 16) (dual of [117656, 117576, 17]-code), using
(64, 64+16, 59158)-Net over F7 — Digital
Digital (64, 80, 59158)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(780, 59158, F7, 16) (dual of [59158, 59078, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(780, 117656, F7, 16) (dual of [117656, 117576, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(779, 117655, F7, 16) (dual of [117655, 117576, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(779, 117649, F7, 16) (dual of [117649, 117570, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(773, 117649, F7, 15) (dual of [117649, 117576, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 117648 = 76−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(70, 6, F7, 0) (dual of [6, 6, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(70, s, F7, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- 1 times code embedding in larger space [i] based on linear OA(779, 117655, F7, 16) (dual of [117655, 117576, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(780, 117656, F7, 16) (dual of [117656, 117576, 17]-code), using
(64, 64+16, large)-Net in Base 7 — Upper bound on s
There is no (64, 80, large)-net in base 7, because
- 14 times m-reduction [i] would yield (64, 66, large)-net in base 7, but