Best Known (90, 106, s)-Nets in Base 7
(90, 106, 720601)-Net over F7 — Constructive and digital
Digital (90, 106, 720601)-net over F7, using
- 71 times duplication [i] based on digital (89, 105, 720601)-net over F7, using
- net defined by OOA [i] based on linear OOA(7105, 720601, F7, 16, 16) (dual of [(720601, 16), 11529511, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(7105, 5764808, F7, 16) (dual of [5764808, 5764703, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(7105, 5764809, F7, 16) (dual of [5764809, 5764704, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(7105, 5764801, F7, 16) (dual of [5764801, 5764696, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 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
- discarding factors / shortening the dual code based on linear OA(7105, 5764809, F7, 16) (dual of [5764809, 5764704, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(7105, 5764808, F7, 16) (dual of [5764808, 5764703, 17]-code), using
- net defined by OOA [i] based on linear OOA(7105, 720601, F7, 16, 16) (dual of [(720601, 16), 11529511, 17]-NRT-code), using
(90, 106, 2882405)-Net over F7 — Digital
Digital (90, 106, 2882405)-net over F7, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(7106, 2882405, F7, 2, 16) (dual of [(2882405, 2), 5764704, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(7106, 5764810, F7, 16) (dual of [5764810, 5764704, 17]-code), using
- 1 times code embedding in larger space [i] based on linear OA(7105, 5764809, F7, 16) (dual of [5764809, 5764704, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(14) [i] based on
- linear OA(7105, 5764801, F7, 16) (dual of [5764801, 5764696, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(797, 5764801, F7, 15) (dual of [5764801, 5764704, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 5764800 = 78−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(70, 8, F7, 0) (dual of [8, 8, 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(7105, 5764809, F7, 16) (dual of [5764809, 5764704, 17]-code), using
- OOA 2-folding [i] based on linear OA(7106, 5764810, F7, 16) (dual of [5764810, 5764704, 17]-code), using
(90, 106, large)-Net in Base 7 — Upper bound on s
There is no (90, 106, large)-net in base 7, because
- 14 times m-reduction [i] would yield (90, 92, large)-net in base 7, but