Best Known (104, 134, s)-Nets in Base 9
(104, 134, 3937)-Net over F9 — Constructive and digital
Digital (104, 134, 3937)-net over F9, using
- 92 times duplication [i] based on digital (102, 132, 3937)-net over F9, using
- net defined by OOA [i] based on linear OOA(9132, 3937, F9, 30, 30) (dual of [(3937, 30), 117978, 31]-NRT-code), using
- OA 15-folding and stacking [i] based on linear OA(9132, 59055, F9, 30) (dual of [59055, 58923, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(9132, 59060, F9, 30) (dual of [59060, 58928, 31]-code), using
- construction X applied to Ce(29) ⊂ Ce(27) [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(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- linear OA(91, 11, F9, 1) (dual of [11, 10, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, s, F9, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(29) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(9132, 59060, F9, 30) (dual of [59060, 58928, 31]-code), using
- OA 15-folding and stacking [i] based on linear OA(9132, 59055, F9, 30) (dual of [59055, 58923, 31]-code), using
- net defined by OOA [i] based on linear OOA(9132, 3937, F9, 30, 30) (dual of [(3937, 30), 117978, 31]-NRT-code), using
(104, 134, 48130)-Net over F9 — Digital
Digital (104, 134, 48130)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9134, 48130, F9, 30) (dual of [48130, 47996, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(9134, 59063, F9, 30) (dual of [59063, 58929, 31]-code), using
- construction XX applied to Ce(29) ⊂ Ce(27) ⊂ Ce(25) [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(9121, 59049, F9, 28) (dual of [59049, 58928, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [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(91, 12, F9, 1) (dual of [12, 11, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- the primitive expurgated narrow-sense BCH-code C(I) with length 728 = 93−1, defining interval I = [0,0], and designed minimum distance d ≥ |I|+1 = 2 [i]
- discarding factors / shortening the dual code based on linear OA(91, 728, F9, 1) (dual of [728, 727, 2]-code), using
- linear OA(91, 2, F9, 1) (dual of [2, 1, 2]-code), using
- dual of repetition code with length 2 [i]
- construction XX applied to Ce(29) ⊂ Ce(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(9134, 59063, F9, 30) (dual of [59063, 58929, 31]-code), using
(104, 134, large)-Net in Base 9 — Upper bound on s
There is no (104, 134, large)-net in base 9, because
- 28 times m-reduction [i] would yield (104, 106, large)-net in base 9, but