Best Known (119, 119+30, s)-Nets in Base 5
(119, 119+30, 1043)-Net over F5 — Constructive and digital
Digital (119, 149, 1043)-net over F5, using
- t-expansion [i] based on digital (118, 149, 1043)-net over F5, using
- net defined by OOA [i] based on linear OOA(5149, 1043, F5, 31, 31) (dual of [(1043, 31), 32184, 32]-NRT-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(5149, 15646, F5, 31) (dual of [15646, 15497, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(5149, 15647, F5, 31) (dual of [15647, 15498, 32]-code), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- linear OA(5145, 15625, F5, 31) (dual of [15625, 15480, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(5127, 15625, F5, 27) (dual of [15625, 15498, 28]-code), using an extension Ce(26) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,26], and designed minimum distance d ≥ |I|+1 = 27 [i]
- linear OA(54, 22, F5, 3) (dual of [22, 18, 4]-code or 22-cap in PG(3,5)), using
- construction X applied to Ce(30) ⊂ Ce(26) [i] based on
- discarding factors / shortening the dual code based on linear OA(5149, 15647, F5, 31) (dual of [15647, 15498, 32]-code), using
- OOA 15-folding and stacking with additional row [i] based on linear OA(5149, 15646, F5, 31) (dual of [15646, 15497, 32]-code), using
- net defined by OOA [i] based on linear OOA(5149, 1043, F5, 31, 31) (dual of [(1043, 31), 32184, 32]-NRT-code), using
(119, 119+30, 13960)-Net over F5 — Digital
Digital (119, 149, 13960)-net over F5, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(5149, 13960, F5, 30) (dual of [13960, 13811, 31]-code), using
- discarding factors / shortening the dual code based on linear OA(5149, 15651, F5, 30) (dual of [15651, 15502, 31]-code), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- linear OA(5145, 15625, F5, 31) (dual of [15625, 15480, 32]-code), using an extension Ce(30) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,30], and designed minimum distance d ≥ |I|+1 = 31 [i]
- linear OA(5121, 15625, F5, 26) (dual of [15625, 15504, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 15624 = 56−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(54, 26, F5, 3) (dual of [26, 22, 4]-code or 26-cap in PG(3,5)), using
- construction X applied to Ce(30) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(5149, 15651, F5, 30) (dual of [15651, 15502, 31]-code), using
(119, 119+30, large)-Net in Base 5 — Upper bound on s
There is no (119, 149, large)-net in base 5, because
- 28 times m-reduction [i] would yield (119, 121, large)-net in base 5, but