Best Known (97, 117, s)-Nets in Base 5
(97, 117, 7815)-Net over F5 — Constructive and digital
Digital (97, 117, 7815)-net over F5, using
- net defined by OOA [i] based on linear OOA(5117, 7815, F5, 20, 20) (dual of [(7815, 20), 156183, 21]-NRT-code), using
- OA 10-folding and stacking [i] based on linear OA(5117, 78150, F5, 20) (dual of [78150, 78033, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5117, 78151, F5, 20) (dual of [78151, 78034, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(5117, 78151, F5, 20) (dual of [78151, 78034, 21]-code), using
- OA 10-folding and stacking [i] based on linear OA(5117, 78150, F5, 20) (dual of [78150, 78033, 21]-code), using
(97, 117, 60319)-Net over F5 — Digital
Digital (97, 117, 60319)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5117, 60319, F5, 20) (dual of [60319, 60202, 21]-code), using
- discarding factors / shortening the dual code based on linear OA(5117, 78151, F5, 20) (dual of [78151, 78034, 21]-code), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- linear OA(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- construction X applied to Ce(20) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(5117, 78151, F5, 20) (dual of [78151, 78034, 21]-code), using
(97, 117, large)-Net in Base 5 — Upper bound on s
There is no (97, 117, large)-net in base 5, because
- 18 times m-reduction [i] would yield (97, 99, large)-net in base 5, but