Best Known (35, 35+10, s)-Nets in Base 9
(35, 35+10, 11813)-Net over F9 — Constructive and digital
Digital (35, 45, 11813)-net over F9, using
- net defined by OOA [i] based on linear OOA(945, 11813, F9, 10, 10) (dual of [(11813, 10), 118085, 11]-NRT-code), using
- OA 5-folding and stacking [i] based on linear OA(945, 59065, F9, 10) (dual of [59065, 59020, 11]-code), using
- discarding factors / shortening the dual code based on linear OA(945, 59068, F9, 10) (dual of [59068, 59023, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- linear OA(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(926, 59049, F9, 6) (dual of [59049, 59023, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(9) ⊂ Ce(5) [i] based on
- discarding factors / shortening the dual code based on linear OA(945, 59068, F9, 10) (dual of [59068, 59023, 11]-code), using
- OA 5-folding and stacking [i] based on linear OA(945, 59065, F9, 10) (dual of [59065, 59020, 11]-code), using
(35, 35+10, 59068)-Net over F9 — Digital
Digital (35, 45, 59068)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(945, 59068, F9, 10) (dual of [59068, 59023, 11]-code), using
- construction X applied to Ce(9) ⊂ Ce(5) [i] based on
- linear OA(941, 59049, F9, 10) (dual of [59049, 59008, 11]-code), using an extension Ce(9) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,9], and designed minimum distance d ≥ |I|+1 = 10 [i]
- linear OA(926, 59049, F9, 6) (dual of [59049, 59023, 7]-code), using an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [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(9) ⊂ Ce(5) [i] based on
(35, 35+10, large)-Net in Base 9 — Upper bound on s
There is no (35, 45, large)-net in base 9, because
- 8 times m-reduction [i] would yield (35, 37, large)-net in base 9, but