Best Known (31, 36, s)-Nets in Base 5
(31, 36, 976561)-Net over F5 — Constructive and digital
Digital (31, 36, 976561)-net over F5, using
- net defined by OOA [i] based on linear OOA(536, 976561, F5, 5, 5) (dual of [(976561, 5), 4882769, 6]-NRT-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(536, 1953123, F5, 5) (dual of [1953123, 1953087, 6]-code), using
- discarding factors / shortening the dual code based on linear OA(536, 1953124, F5, 5) (dual of [1953124, 1953088, 6]-code), using
- 1 times truncation [i] based on linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 1 times truncation [i] based on linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using
- discarding factors / shortening the dual code based on linear OA(536, 1953124, F5, 5) (dual of [1953124, 1953088, 6]-code), using
- OOA 2-folding and stacking with additional row [i] based on linear OA(536, 1953123, F5, 5) (dual of [1953123, 1953087, 6]-code), using
(31, 36, 1953124)-Net over F5 — Digital
Digital (31, 36, 1953124)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(536, 1953124, F5, 5) (dual of [1953124, 1953088, 6]-code), using
- 1 times truncation [i] based on linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using
- an extension Ce(5) of the primitive narrow-sense BCH-code C(I) with length 1953124 = 59−1, defining interval I = [1,5], and designed minimum distance d ≥ |I|+1 = 6 [i]
- 1 times truncation [i] based on linear OA(537, 1953125, F5, 6) (dual of [1953125, 1953088, 7]-code), using
(31, 36, large)-Net in Base 5 — Upper bound on s
There is no (31, 36, large)-net in base 5, because
- 3 times m-reduction [i] would yield (31, 33, large)-net in base 5, but