Best Known (94, 94+28, s)-Nets in Base 9
(94, 94+28, 4218)-Net over F9 — Constructive and digital
Digital (94, 122, 4218)-net over F9, using
- net defined by OOA [i] based on linear OOA(9122, 4218, F9, 28, 28) (dual of [(4218, 28), 117982, 29]-NRT-code), using
- OA 14-folding and stacking [i] based on linear OA(9122, 59052, F9, 28) (dual of [59052, 58930, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9122, 59055, F9, 28) (dual of [59055, 58933, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- 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, 6, F9, 1) (dual of [6, 5, 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(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(9122, 59055, F9, 28) (dual of [59055, 58933, 29]-code), using
- OA 14-folding and stacking [i] based on linear OA(9122, 59052, F9, 28) (dual of [59052, 58930, 29]-code), using
(94, 94+28, 36385)-Net over F9 — Digital
Digital (94, 122, 36385)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9122, 36385, F9, 28) (dual of [36385, 36263, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(9122, 59055, F9, 28) (dual of [59055, 58933, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- 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, 6, F9, 1) (dual of [6, 5, 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(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(9122, 59055, F9, 28) (dual of [59055, 58933, 29]-code), using
(94, 94+28, large)-Net in Base 9 — Upper bound on s
There is no (94, 122, large)-net in base 9, because
- 26 times m-reduction [i] would yield (94, 96, large)-net in base 9, but