Best Known (85−16, 85, s)-Nets in Base 5
(85−16, 85, 9765)-Net over F5 — Constructive and digital
Digital (69, 85, 9765)-net over F5, using
- net defined by OOA [i] based on linear OOA(585, 9765, F5, 16, 16) (dual of [(9765, 16), 156155, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(585, 78120, F5, 16) (dual of [78120, 78035, 17]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(585, 78120, F5, 16) (dual of [78120, 78035, 17]-code), using
(85−16, 85, 39062)-Net over F5 — Digital
Digital (69, 85, 39062)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(585, 39062, F5, 2, 16) (dual of [(39062, 2), 78039, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(585, 78124, F5, 16) (dual of [78124, 78039, 17]-code), using
- discarding factors / shortening the dual code based on 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]
- discarding factors / shortening the dual code based on linear OA(585, 78125, F5, 16) (dual of [78125, 78040, 17]-code), using
- OOA 2-folding [i] based on linear OA(585, 78124, F5, 16) (dual of [78124, 78039, 17]-code), using
(85−16, 85, large)-Net in Base 5 — Upper bound on s
There is no (69, 85, large)-net in base 5, because
- 14 times m-reduction [i] would yield (69, 71, large)-net in base 5, but