Best Known (121, 145, s)-Nets in Base 5
(121, 145, 6514)-Net over F5 — Constructive and digital
Digital (121, 145, 6514)-net over F5, using
- 52 times duplication [i] based on digital (119, 143, 6514)-net over F5, using
- net defined by OOA [i] based on linear OOA(5143, 6514, F5, 24, 24) (dual of [(6514, 24), 156193, 25]-NRT-code), using
- OA 12-folding and stacking [i] based on linear OA(5143, 78168, F5, 24) (dual of [78168, 78025, 25]-code), using
- discarding factors / shortening the dual code based on linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- discarding factors / shortening the dual code based on linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
- OA 12-folding and stacking [i] based on linear OA(5143, 78168, F5, 24) (dual of [78168, 78025, 25]-code), using
- net defined by OOA [i] based on linear OOA(5143, 6514, F5, 24, 24) (dual of [(6514, 24), 156193, 25]-NRT-code), using
(121, 145, 78173)-Net over F5 — Digital
Digital (121, 145, 78173)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5145, 78173, F5, 24) (dual of [78173, 78028, 25]-code), using
- construction X with Varšamov bound [i] based on
- linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(5134, 78125, F5, 24) (dual of [78125, 77991, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(599, 78125, F5, 18) (dual of [78125, 78026, 19]-code), using an extension Ce(17) of the primitive narrow-sense BCH-code C(I) with length 78124 = 57−1, defining interval I = [1,17], and designed minimum distance d ≥ |I|+1 = 18 [i]
- linear OA(59, 44, F5, 5) (dual of [44, 35, 6]-code), using
- construction X applied to Ce(23) ⊂ Ce(17) [i] based on
- linear OA(5143, 78171, F5, 23) (dual of [78171, 78028, 24]-code), using Gilbert–Varšamov bound and bm = 5143 > Vbs−1(k−1) = 6921 221455 152285 996076 946862 556983 443115 631603 705421 537631 792117 669609 631930 843878 869911 655182 268345 [i]
- linear OA(50, 2, F5, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(50, s, F5, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(5143, 78169, F5, 24) (dual of [78169, 78026, 25]-code), using
- construction X with Varšamov bound [i] based on
(121, 145, large)-Net in Base 5 — Upper bound on s
There is no (121, 145, large)-net in base 5, because
- 22 times m-reduction [i] would yield (121, 123, large)-net in base 5, but