Best Known (86, 102, s)-Nets in Base 5
(86, 102, 48831)-Net over F5 — Constructive and digital
Digital (86, 102, 48831)-net over F5, using
- 51 times duplication [i] based on digital (85, 101, 48831)-net over F5, using
- net defined by OOA [i] based on linear OOA(5101, 48831, F5, 16, 16) (dual of [(48831, 16), 781195, 17]-NRT-code), using
- OA 8-folding and stacking [i] based on linear OA(5101, 390648, F5, 16) (dual of [390648, 390547, 17]-code), using
- discarding factors / shortening the dual code based on linear OA(5101, 390651, F5, 16) (dual of [390651, 390550, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [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(15) ⊂ Ce(11) [i] based on
- discarding factors / shortening the dual code based on linear OA(5101, 390651, F5, 16) (dual of [390651, 390550, 17]-code), using
- OA 8-folding and stacking [i] based on linear OA(5101, 390648, F5, 16) (dual of [390648, 390547, 17]-code), using
- net defined by OOA [i] based on linear OOA(5101, 48831, F5, 16, 16) (dual of [(48831, 16), 781195, 17]-NRT-code), using
(86, 102, 195327)-Net over F5 — Digital
Digital (86, 102, 195327)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(5102, 195327, F5, 2, 16) (dual of [(195327, 2), 390552, 17]-NRT-code), using
- OOA 2-folding [i] based on linear OA(5102, 390654, F5, 16) (dual of [390654, 390552, 17]-code), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- linear OA(597, 390625, F5, 16) (dual of [390625, 390528, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(573, 390625, F5, 12) (dual of [390625, 390552, 13]-code), using an extension Ce(11) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,11], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(55, 29, F5, 3) (dual of [29, 24, 4]-code or 29-cap in PG(4,5)), using
- discarding factors / shortening the dual code based on linear OA(55, 42, F5, 3) (dual of [42, 37, 4]-code or 42-cap in PG(4,5)), using
- construction X applied to Ce(15) ⊂ Ce(11) [i] based on
- OOA 2-folding [i] based on linear OA(5102, 390654, F5, 16) (dual of [390654, 390552, 17]-code), using
(86, 102, large)-Net in Base 5 — Upper bound on s
There is no (86, 102, large)-net in base 5, because
- 14 times m-reduction [i] would yield (86, 88, large)-net in base 5, but