Best Known (84−18, 84, s)-Nets in Base 9
(84−18, 84, 6563)-Net over F9 — Constructive and digital
Digital (66, 84, 6563)-net over F9, using
- net defined by OOA [i] based on linear OOA(984, 6563, F9, 18, 18) (dual of [(6563, 18), 118050, 19]-NRT-code), using
- OA 9-folding and stacking [i] based on linear OA(984, 59067, F9, 18) (dual of [59067, 58983, 19]-code), using
- 1 times truncation [i] based on linear OA(985, 59068, F9, 19) (dual of [59068, 58983, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(981, 59049, F9, 19) (dual of [59049, 58968, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(966, 59049, F9, 15) (dual of [59049, 58983, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(985, 59068, F9, 19) (dual of [59068, 58983, 20]-code), using
- OA 9-folding and stacking [i] based on linear OA(984, 59067, F9, 18) (dual of [59067, 58983, 19]-code), using
(84−18, 84, 59067)-Net over F9 — Digital
Digital (66, 84, 59067)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(984, 59067, F9, 18) (dual of [59067, 58983, 19]-code), using
- 1 times truncation [i] based on linear OA(985, 59068, F9, 19) (dual of [59068, 58983, 20]-code), using
- construction X applied to Ce(18) ⊂ Ce(14) [i] based on
- linear OA(981, 59049, F9, 19) (dual of [59049, 58968, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(966, 59049, F9, 15) (dual of [59049, 58983, 16]-code), using an extension Ce(14) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,14], and designed minimum distance d ≥ |I|+1 = 15 [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(18) ⊂ Ce(14) [i] based on
- 1 times truncation [i] based on linear OA(985, 59068, F9, 19) (dual of [59068, 58983, 20]-code), using
(84−18, 84, large)-Net in Base 9 — Upper bound on s
There is no (66, 84, large)-net in base 9, because
- 16 times m-reduction [i] would yield (66, 68, large)-net in base 9, but