Best Known (110, 110+30, s)-Nets in Base 9
(110, 110+30, 3938)-Net over F9 — Constructive and digital
Digital (110, 140, 3938)-net over F9, using
- 94 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
(110, 110+30, 59088)-Net over F9 — Digital
Digital (110, 140, 59088)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9140, 59088, F9, 30) (dual of [59088, 58948, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [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(9101, 59049, F9, 23) (dual of [59049, 58948, 24]-code), using an extension Ce(22) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,22], and designed minimum distance d ≥ |I|+1 = 23 [i]
- linear OA(99, 39, F9, 6) (dual of [39, 30, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(99, 41, F9, 6) (dual of [41, 32, 7]-code), using
- a “GraCyc†code from Grassl’s database [i]
- discarding factors / shortening the dual code based on linear OA(99, 41, F9, 6) (dual of [41, 32, 7]-code), using
- construction X applied to Ce(29) ⊂ Ce(22) [i] based on
(110, 110+30, large)-Net in Base 9 — Upper bound on s
There is no (110, 140, large)-net in base 9, because
- 28 times m-reduction [i] would yield (110, 112, large)-net in base 9, but