Best Known (119, 144, s)-Nets in Base 5
(119, 144, 6512)-Net over F5 — Constructive and digital
Digital (119, 144, 6512)-net over F5, using
- net defined by OOA [i] based on linear OOA(5144, 6512, F5, 25, 25) (dual of [(6512, 25), 162656, 26]-NRT-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5144, 78145, F5, 25) (dual of [78145, 78001, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 78149, F5, 25) (dual of [78149, 78005, 26]-code), using
- 1 times truncation [i] based on linear OA(5145, 78150, F5, 26) (dual of [78150, 78005, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [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(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [i] based on
- 1 times truncation [i] based on linear OA(5145, 78150, F5, 26) (dual of [78150, 78005, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 78149, F5, 25) (dual of [78149, 78005, 26]-code), using
- OOA 12-folding and stacking with additional row [i] based on linear OA(5144, 78145, F5, 25) (dual of [78145, 78001, 26]-code), using
(119, 144, 52243)-Net over F5 — Digital
Digital (119, 144, 52243)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5144, 52243, F5, 25) (dual of [52243, 52099, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 78149, F5, 25) (dual of [78149, 78005, 26]-code), using
- 1 times truncation [i] based on linear OA(5145, 78150, F5, 26) (dual of [78150, 78005, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(21) [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(5120, 78125, F5, 22) (dual of [78125, 78005, 23]-code), using an extension Ce(21) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,21], and designed minimum distance d ≥ |I|+1 = 22 [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(25) ⊂ Ce(21) [i] based on
- 1 times truncation [i] based on linear OA(5145, 78150, F5, 26) (dual of [78150, 78005, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5144, 78149, F5, 25) (dual of [78149, 78005, 26]-code), using
(119, 144, large)-Net in Base 5 — Upper bound on s
There is no (119, 144, large)-net in base 5, because
- 23 times m-reduction [i] would yield (119, 121, large)-net in base 5, but