Best Known (72, 72+19, s)-Nets in Base 5
(72, 72+19, 1736)-Net over F5 — Constructive and digital
Digital (72, 91, 1736)-net over F5, using
- net defined by OOA [i] based on linear OOA(591, 1736, F5, 19, 19) (dual of [(1736, 19), 32893, 20]-NRT-code), using
- OOA 9-folding and stacking with additional row [i] based on linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- OOA 9-folding and stacking with additional row [i] based on linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using
(72, 72+19, 8990)-Net over F5 — Digital
Digital (72, 91, 8990)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(591, 8990, F5, 19) (dual of [8990, 8899, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using
- an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(591, 15625, F5, 19) (dual of [15625, 15534, 20]-code), using
(72, 72+19, large)-Net in Base 5 — Upper bound on s
There is no (72, 91, large)-net in base 5, because
- 17 times m-reduction [i] would yield (72, 74, large)-net in base 5, but