Best Known (76−16, 76, s)-Nets in Base 9
(76−16, 76, 7384)-Net over F9 — Constructive and digital
Digital (60, 76, 7384)-net over F9, using
- 91 times duplication [i] based on digital (59, 75, 7384)-net over F9, using
- net defined by OOA [i] based on linear OOA(975, 7384, F9, 16, 16) (dual of [(7384, 16), 118069, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(975, 59072, F9, 16) (dual of [59072, 58997, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(975, 59073, F9, 16) (dual of [59073, 58998, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(971, 59049, F9, 16) (dual of [59049, 58978, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(951, 59049, F9, 12) (dual of [59049, 58998, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(975, 59073, F9, 16) (dual of [59073, 58998, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(975, 59072, F9, 16) (dual of [59072, 58997, 17]-code), using
- net defined by OOA [i] based on linear OOA(975, 7384, F9, 16, 16) (dual of [(7384, 16), 118069, 17]-NRT-code), using
(76−16, 76, 59075)-Net over F9 — Digital
Digital (60, 76, 59075)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(976, 59075, F9, 16) (dual of [59075, 58999, 17]-code), using
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
- linear OA(971, 59049, F9, 16) (dual of [59049, 58978, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(951, 59049, F9, 12) (dual of [59049, 58998, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(946, 59049, F9, 11) (dual of [59049, 59003, 12]-code), using an extension Ce(10) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,10], and designed minimum distance d ≥ |I|+1 = 11 [i]
- linear OA(94, 25, F9, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,9)), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(15) ⊂ Ce(11) ⊂ Ce(10) [i] based on
(76−16, 76, large)-Net in Base 9 — Upper bound on s
There is no (60, 76, large)-net in base 9, because
- 14 times m-reduction [i] would yield (60, 62, large)-net in base 9, but