Best Known (97, 97+29, s)-Nets in Base 9
(97, 97+29, 4218)-Net over F9 — Constructive and digital
Digital (97, 126, 4218)-net over F9, using
- net defined by OOA [i] based on linear OOA(9126, 4218, F9, 29, 29) (dual of [(4218, 29), 122196, 30]-NRT-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(9126, 59053, F9, 29) (dual of [59053, 58927, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(9126, 59054, F9, 29) (dual of [59054, 58928, 30]-code), using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- linear OA(9126, 59049, F9, 29) (dual of [59049, 58923, 30]-code), using an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [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(90, 5, F9, 0) (dual of [5, 5, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(90, s, F9, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(28) ⊂ Ce(27) [i] based on
- discarding factors / shortening the dual code based on linear OA(9126, 59054, F9, 29) (dual of [59054, 58928, 30]-code), using
- OOA 14-folding and stacking with additional row [i] based on linear OA(9126, 59053, F9, 29) (dual of [59053, 58927, 30]-code), using
(97, 97+29, 35720)-Net over F9 — Digital
Digital (97, 126, 35720)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9126, 35720, F9, 29) (dual of [35720, 35594, 30]-code), using
- discarding factors / shortening the dual code based on linear OA(9126, 59049, F9, 29) (dual of [59049, 58923, 30]-code), using
- an extension Ce(28) of the primitive narrow-sense BCH-code C(I) with length 59048 = 95−1, defining interval I = [1,28], and designed minimum distance d ≥ |I|+1 = 29 [i]
- discarding factors / shortening the dual code based on linear OA(9126, 59049, F9, 29) (dual of [59049, 58923, 30]-code), using
(97, 97+29, large)-Net in Base 9 — Upper bound on s
There is no (97, 126, large)-net in base 9, because
- 27 times m-reduction [i] would yield (97, 99, large)-net in base 9, but