Best Known (62, 62+13, s)-Nets in Base 5
(62, 62+13, 13024)-Net over F5 — Constructive and digital
Digital (62, 75, 13024)-net over F5, using
- net defined by OOA [i] based on linear OOA(575, 13024, F5, 13, 13) (dual of [(13024, 13), 169237, 14]-NRT-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(575, 78145, F5, 13) (dual of [78145, 78070, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(575, 78150, F5, 13) (dual of [78150, 78075, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(575, 78150, F5, 13) (dual of [78150, 78075, 14]-code), using
- OOA 6-folding and stacking with additional row [i] based on linear OA(575, 78145, F5, 13) (dual of [78145, 78070, 14]-code), using
(62, 62+13, 61811)-Net over F5 — Digital
Digital (62, 75, 61811)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(575, 61811, F5, 13) (dual of [61811, 61736, 14]-code), using
- discarding factors / shortening the dual code based on linear OA(575, 78150, F5, 13) (dual of [78150, 78075, 14]-code), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- linear OA(571, 78125, F5, 13) (dual of [78125, 78054, 14]-code), using an extension Ce(12) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(550, 78125, F5, 9) (dual of [78125, 78075, 10]-code), using an extension Ce(8) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,8], and designed minimum distance d ≥ |I|+1 = 9 [i]
- linear OA(54, 25, F5, 3) (dual of [25, 21, 4]-code or 25-cap in PG(3,5)), using
- construction X applied to Ce(12) ⊂ Ce(8) [i] based on
- discarding factors / shortening the dual code based on linear OA(575, 78150, F5, 13) (dual of [78150, 78075, 14]-code), using
(62, 62+13, large)-Net in Base 5 — Upper bound on s
There is no (62, 75, large)-net in base 5, because
- 11 times m-reduction [i] would yield (62, 64, large)-net in base 5, but