Best Known (76, 76+17, s)-Nets in Base 5
(76, 76+17, 9766)-Net over F5 — Constructive and digital
Digital (76, 93, 9766)-net over F5, using
- 51 times duplication [i] based on digital (75, 92, 9766)-net over F5, using
- net defined by OOA [i] based on linear OOA(592, 9766, F5, 17, 17) (dual of [(9766, 17), 165930, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(592, 78129, F5, 17) (dual of [78129, 78037, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(592, 78132, F5, 17) (dual of [78132, 78040, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(50, 7, F5, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- discarding factors / shortening the dual code based on linear OA(592, 78132, F5, 17) (dual of [78132, 78040, 18]-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(592, 78129, F5, 17) (dual of [78129, 78037, 18]-code), using
- net defined by OOA [i] based on linear OOA(592, 9766, F5, 17, 17) (dual of [(9766, 17), 165930, 18]-NRT-code), using
(76, 76+17, 39066)-Net over F5 — Digital
Digital (76, 93, 39066)-net over F5, using
- 51 times duplication [i] based on digital (75, 92, 39066)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(592, 39066, F5, 2, 17) (dual of [(39066, 2), 78040, 18]-NRT-code), using
- OOA 2-folding [i] based on linear OA(592, 78132, F5, 17) (dual of [78132, 78040, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(592, 78125, F5, 17) (dual of [78125, 78033, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [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(50, 7, F5, 0) (dual of [7, 7, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- OOA 2-folding [i] based on linear OA(592, 78132, F5, 17) (dual of [78132, 78040, 18]-code), using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(592, 39066, F5, 2, 17) (dual of [(39066, 2), 78040, 18]-NRT-code), using
(76, 76+17, large)-Net in Base 5 — Upper bound on s
There is no (76, 93, large)-net in base 5, because
- 15 times m-reduction [i] would yield (76, 78, large)-net in base 5, but