Best Known (83, 107, s)-Nets in Base 9
(83, 107, 4921)-Net over F9 — Constructive and digital
Digital (83, 107, 4921)-net over F9, using
- 91 times duplication [i] based on digital (82, 106, 4921)-net over F9, using
- net defined by OOA [i] based on linear OOA(9106, 4921, F9, 24, 24) (dual of [(4921, 24), 117998, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(9106, 59052, F9, 24) (dual of [59052, 58946, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9106, 59054, F9, 24) (dual of [59054, 58948, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- linear OA(9106, 59049, F9, 24) (dual of [59049, 58943, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(22) [i] based on
- discarding factors / shortening the dual code based on linear OA(9106, 59054, F9, 24) (dual of [59054, 58948, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(9106, 59052, F9, 24) (dual of [59052, 58946, 25]-code), using
- net defined by OOA [i] based on linear OOA(9106, 4921, F9, 24, 24) (dual of [(4921, 24), 117998, 25]-NRT-code), using
(83, 107, 44808)-Net over F9 — Digital
Digital (83, 107, 44808)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9107, 44808, F9, 24) (dual of [44808, 44701, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(9107, 59060, F9, 24) (dual of [59060, 58953, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- linear OA(9106, 59049, F9, 24) (dual of [59049, 58943, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(996, 59049, F9, 22) (dual of [59049, 58953, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(23) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(9107, 59060, F9, 24) (dual of [59060, 58953, 25]-code), using
(83, 107, large)-Net in Base 9 — Upper bound on s
There is no (83, 107, large)-net in base 9, because
- 22 times m-reduction [i] would yield (83, 85, large)-net in base 9, but