Best Known (150−25, 150, s)-Nets in Base 5
(150−25, 150, 6514)-Net over F5 — Constructive and digital
Digital (125, 150, 6514)-net over F5, using
- net defined by OOA [i] based on linear OOA(5150, 6514, F5, 25, 25) (dual of [(6514, 25), 162700, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5150, 78169, F5, 25) (dual of [78169, 78019, 26]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5141, 78125, F5, 26) (dual of [78125, 77984, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- OOA 12-folding and stacking with additional row [i] based on linear OA(5150, 78169, F5, 25) (dual of [78169, 78019, 26]-code), using
(150−25, 150, 78169)-Net over F5 — Digital
Digital (125, 150, 78169)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5150, 78169, F5, 25) (dual of [78169, 78019, 26]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- linear OA(5141, 78125, F5, 26) (dual of [78125, 77984, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(5106, 78125, F5, 19) (dual of [78125, 78019, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
(150−25, 150, large)-Net in Base 5 — Upper bound on s
There is no (125, 150, large)-net in base 5, because
- 23 times m-reduction [i] would yield (125, 127, large)-net in base 5, but