Best Known (120−26, 120, s)-Nets in Base 9
(120−26, 120, 4544)-Net over F9 — Constructive and digital
Digital (94, 120, 4544)-net over F9, using
- net defined by OOA [i] based on linear OOA(9120, 4544, F9, 26, 26) (dual of [(4544, 26), 118024, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(9120, 59072, F9, 26) (dual of [59072, 58952, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(9120, 59073, F9, 26) (dual of [59073, 58953, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- discarding factors / shortening the dual code based on linear OA(9120, 59073, F9, 26) (dual of [59073, 58953, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(9120, 59072, F9, 26) (dual of [59072, 58952, 27]-code), using
(120−26, 120, 59073)-Net over F9 — Digital
Digital (94, 120, 59073)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9120, 59073, F9, 26) (dual of [59073, 58953, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [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(94, 24, F9, 3) (dual of [24, 20, 4]-code or 24-cap in PG(3,9)), using
- construction X applied to Ce(25) ⊂ Ce(21) [i] based on
(120−26, 120, large)-Net in Base 9 — Upper bound on s
There is no (94, 120, large)-net in base 9, because
- 24 times m-reduction [i] would yield (94, 96, large)-net in base 9, but