Best Known (63, 63+17, s)-Nets in Base 9
(63, 63+17, 7384)-Net over F9 — Constructive and digital
Digital (63, 80, 7384)-net over F9, using
- net defined by OOA [i] based on linear OOA(980, 7384, F9, 17, 17) (dual of [(7384, 17), 125448, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(980, 59073, F9, 17) (dual of [59073, 58993, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(980, 59073, F9, 17) (dual of [59073, 58993, 18]-code), using
(63, 63+17, 59073)-Net over F9 — Digital
Digital (63, 80, 59073)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(980, 59073, F9, 17) (dual of [59073, 58993, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(976, 59049, F9, 17) (dual of [59049, 58973, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(956, 59049, F9, 13) (dual of [59049, 58993, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [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(16) ⊂ Ce(12) [i] based on
(63, 63+17, large)-Net in Base 9 — Upper bound on s
There is no (63, 80, large)-net in base 9, because
- 15 times m-reduction [i] would yield (63, 65, large)-net in base 9, but