Best Known (33−6, 33, s)-Nets in Base 5
(33−6, 33, 130208)-Net over F5 — Constructive and digital
Digital (27, 33, 130208)-net over F5, using
- net defined by OOA [i] based on linear OOA(533, 130208, F5, 6, 6) (dual of [(130208, 6), 781215, 7]-NRT-code), using
- OA 3-folding and stacking [i] based on linear OA(533, 390624, F5, 6) (dual of [390624, 390591, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using
- OA 3-folding and stacking [i] based on linear OA(533, 390624, F5, 6) (dual of [390624, 390591, 7]-code), using
(33−6, 33, 216147)-Net over F5 — Digital
Digital (27, 33, 216147)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(533, 216147, F5, 6) (dual of [216147, 216114, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 390624 = 58−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- discarding factors / shortening the dual code based on linear OA(533, 390625, F5, 6) (dual of [390625, 390592, 7]-code), using
(33−6, 33, large)-Net in Base 5 — Upper bound on s
There is no (27, 33, large)-net in base 5, because
- 4 times m-reduction [i] would yield (27, 29, large)-net in base 5, but