Best Known (94, 94+17, s)-Nets in Base 9
(94, 94+17, 597875)-Net over F9 — Constructive and digital
Digital (94, 111, 597875)-net over F9, using
- 91 times duplication [i] based on digital (93, 110, 597875)-net over F9, using
- net defined by OOA [i] based on linear OOA(9110, 597875, F9, 17, 17) (dual of [(597875, 17), 10163765, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- OOA 8-folding and stacking with additional row [i] based on linear OA(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
- net defined by OOA [i] based on linear OOA(9110, 597875, F9, 17, 17) (dual of [(597875, 17), 10163765, 18]-NRT-code), using
(94, 94+17, 4783003)-Net over F9 — Digital
Digital (94, 111, 4783003)-net over F9, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(9111, 4783003, F9, 17) (dual of [4783003, 4782892, 18]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(9106, 4782969, F9, 17) (dual of [4782969, 4782863, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(978, 4782969, F9, 13) (dual of [4782969, 4782891, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 4782968 = 97−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(94, 32, F9, 3) (dual of [32, 28, 4]-code or 32-cap in PG(3,9)), using
- construction X applied to Ce(16) ⊂ Ce(12) [i] based on
- linear OA(9110, 4783002, F9, 16) (dual of [4783002, 4782892, 17]-code), using Gilbert–Varšamov bound and bm = 9110 > Vbs−1(k−1) = 422034 451883 037198 745147 407448 575628 556722 525695 672473 399458 292135 467570 013889 673550 996053 166224 420809 [i]
- linear OA(90, 1, F9, 0) (dual of [1, 1, 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
- linear OA(9110, 4783001, F9, 17) (dual of [4783001, 4782891, 18]-code), using
- construction X with Varšamov bound [i] based on
(94, 94+17, large)-Net in Base 9 — Upper bound on s
There is no (94, 111, large)-net in base 9, because
- 15 times m-reduction [i] would yield (94, 96, large)-net in base 9, but