Best Known (146−26, 146, s)-Nets in Base 5
(146−26, 146, 6011)-Net over F5 — Constructive and digital
Digital (120, 146, 6011)-net over F5, using
- 51 times duplication [i] based on digital (119, 145, 6011)-net over F5, using
- net defined by OOA [i] based on linear OOA(5145, 6011, F5, 26, 26) (dual of [(6011, 26), 156141, 27]-NRT-code), using
- OA 13-folding and stacking [i] based on linear OA(5145, 78143, F5, 26) (dual of [78143, 77998, 27]-code), using
- discarding factors / shortening the dual code 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
- discarding factors / shortening the dual code based on linear OA(5145, 78150, F5, 26) (dual of [78150, 78005, 27]-code), using
- OA 13-folding and stacking [i] based on linear OA(5145, 78143, F5, 26) (dual of [78143, 77998, 27]-code), using
- net defined by OOA [i] based on linear OOA(5145, 6011, F5, 26, 26) (dual of [(6011, 26), 156141, 27]-NRT-code), using
(146−26, 146, 40932)-Net over F5 — Digital
Digital (120, 146, 40932)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5146, 40932, F5, 26) (dual of [40932, 40786, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(5146, 78152, F5, 26) (dual of [78152, 78006, 27]-code), using
- construction XX applied to Ce(25) ⊂ Ce(21) ⊂ Ce(20) [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(5113, 78125, F5, 21) (dual of [78125, 78012, 22]-code), using an extension Ce(20) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,20], and designed minimum distance d ≥ |I|+1 = 21 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- linear OA(50, 1, F5, 0) (dual of [1, 1, 1]-code), using
- dual of repetition code with length 1 [i]
- construction XX applied to Ce(25) ⊂ Ce(21) ⊂ Ce(20) [i] based on
- discarding factors / shortening the dual code based on linear OA(5146, 78152, F5, 26) (dual of [78152, 78006, 27]-code), using
(146−26, 146, large)-Net in Base 5 — Upper bound on s
There is no (120, 146, large)-net in base 5, because
- 24 times m-reduction [i] would yield (120, 122, large)-net in base 5, but