Best Known (107, 107+30, s)-Nets in Base 9
(107, 107+30, 3938)-Net over F9 — Constructive and digital
Digital (107, 137, 3938)-net over F9, using
- 91 times duplication [i] based on digital (106, 136, 3938)-net over F9, using
- net defined by OOA [i] based on linear OOA(9136, 3938, F9, 30, 30) (dual of [(3938, 30), 118004, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(9136, 59070, F9, 30) (dual of [59070, 58934, 31]-code), using
- construction XX applied to Ce(29) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(9116, 59049, F9, 26) (dual of [59049, 58933, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(9111, 59049, F9, 25) (dual of [59049, 58938, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [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(29) ⊂ Ce(25) ⊂ Ce(24) [i] based on
- OA 15-folding and stacking [i] based on linear OA(9136, 59070, F9, 30) (dual of [59070, 58934, 31]-code), using
- net defined by OOA [i] based on linear OOA(9136, 3938, F9, 30, 30) (dual of [(3938, 30), 118004, 31]-NRT-code), using
(107, 107+30, 59075)-Net over F9 — Digital
Digital (107, 137, 59075)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9137, 59075, F9, 30) (dual of [59075, 58938, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
- linear OA(9131, 59049, F9, 30) (dual of [59049, 58918, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(9111, 59049, F9, 25) (dual of [59049, 58938, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(96, 26, F9, 4) (dual of [26, 20, 5]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- 1 times truncation [i] based on linear OA(97, 73, F9, 5) (dual of [73, 66, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(96, 72, F9, 4) (dual of [72, 66, 5]-code), using
- construction X applied to Ce(29) ⊂ Ce(24) [i] based on
(107, 107+30, large)-Net in Base 9 — Upper bound on s
There is no (107, 137, large)-net in base 9, because
- 28 times m-reduction [i] would yield (107, 109, large)-net in base 9, but