Best Known (44, 44+12, s)-Nets in Base 9
(44, 44+12, 9845)-Net over F9 — Constructive and digital
Digital (44, 56, 9845)-net over F9, using
- net defined by OOA [i] based on linear OOA(956, 9845, F9, 12, 12) (dual of [(9845, 12), 118084, 13]-NRT-code), using
- OA 6-folding and stacking [i] based on linear OA(956, 59070, F9, 12) (dual of [59070, 59014, 13]-code), using
- construction XX applied to Ce(11) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- linear OA(951, 59049, F9, 12) (dual of [59049, 58998, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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, 20, F9, 3) (dual of [20, 16, 4]-code or 20-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(956, 59070, F9, 12) (dual of [59070, 59014, 13]-code), using
(44, 44+12, 59070)-Net over F9 — Digital
Digital (44, 56, 59070)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(956, 59070, F9, 12) (dual of [59070, 59014, 13]-code), using
- construction XX applied to Ce(11) ⊂ Ce(7) ⊂ Ce(6) [i] based on
- linear OA(951, 59049, F9, 12) (dual of [59049, 58998, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(936, 59049, F9, 8) (dual of [59049, 59013, 9]-code), using an extension Ce(7) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,7], and designed minimum distance d ≥ |I|+1 = 8 [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, 20, F9, 3) (dual of [20, 16, 4]-code or 20-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
(44, 44+12, large)-Net in Base 9 — Upper bound on s
There is no (44, 56, large)-net in base 9, because
- 10 times m-reduction [i] would yield (44, 46, large)-net in base 9, but