Best Known (39, 50, s)-Nets in Base 9
(39, 50, 11813)-Net over F9 — Constructive and digital
Digital (39, 50, 11813)-net over F9, using
- net defined by OOA [i] based on linear OOA(950, 11813, F9, 11, 11) (dual of [(11813, 11), 129893, 12]-NRT-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(950, 59066, F9, 11) (dual of [59066, 59016, 12]-code), using
- discarding factors / shortening the dual code based on linear OA(950, 59068, F9, 11) (dual of [59068, 59018, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- 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(931, 59049, F9, 7) (dual of [59049, 59018, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(94, 19, F9, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,9)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- discarding factors / shortening the dual code based on linear OA(950, 59068, F9, 11) (dual of [59068, 59018, 12]-code), using
- OOA 5-folding and stacking with additional row [i] based on linear OA(950, 59066, F9, 11) (dual of [59066, 59016, 12]-code), using
(39, 50, 59068)-Net over F9 — Digital
Digital (39, 50, 59068)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(950, 59068, F9, 11) (dual of [59068, 59018, 12]-code), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
- 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(931, 59049, F9, 7) (dual of [59049, 59018, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(94, 19, F9, 3) (dual of [19, 15, 4]-code or 19-cap in PG(3,9)), using
- construction X applied to Ce(10) ⊂ Ce(6) [i] based on
(39, 50, large)-Net in Base 9 — Upper bound on s
There is no (39, 50, large)-net in base 9, because
- 9 times m-reduction [i] would yield (39, 41, large)-net in base 9, but