Best Known (64, 64+12, s)-Nets in Base 9
(64, 64+12, 797166)-Net over F9 — Constructive and digital
Digital (64, 76, 797166)-net over F9, using
- net defined by OOA [i] based on linear OOA(976, 797166, F9, 12, 12) (dual of [(797166, 12), 9565916, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(976, 4782996, F9, 12) (dual of [4782996, 4782920, 13]-code), using
- construction XX applied to Ce(11) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(950, 4782969, F9, 8) (dual of [4782969, 4782919, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(943, 4782969, F9, 7) (dual of [4782969, 4782926, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(94, 26, F9, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,9)), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(11) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- OA 6-folding and stacking [i] based on linear OA(976, 4782996, F9, 12) (dual of [4782996, 4782920, 13]-code), using
(64, 64+12, 4782996)-Net over F9 — Digital
Digital (64, 76, 4782996)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(976, 4782996, F9, 12) (dual of [4782996, 4782920, 13]-code), using
- construction XX applied to Ce(11) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- linear OA(971, 4782969, F9, 12) (dual of [4782969, 4782898, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(950, 4782969, F9, 8) (dual of [4782969, 4782919, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [i]
- linear OA(943, 4782969, F9, 7) (dual of [4782969, 4782926, 8]-code), using an extension Ce(6) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,6], and designed minimum distance d ≥ |I|+1 = 7 [i]
- linear OA(94, 26, F9, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,9)), using
- linear OA(90, 1, F9, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(11) ⊂ Ce(7) ⊂ Ce(6) [i] based on
(64, 64+12, large)-Net in Base 9 — Upper bound on s
There is no (64, 76, large)-net in base 9, because
- 10 times m-reduction [i] would yield (64, 66, large)-net in base 9, but