Best Known (25, 42, s)-Nets in Base 49
(25, 42, 351)-Net over F49 — Constructive and digital
Digital (25, 42, 351)-net over F49, using
- (u, u+v)-construction [i] based on
- digital (1, 9, 51)-net over F49, using
- net from sequence [i] based on digital (1, 50)-sequence over F49, using
- digital (16, 33, 300)-net over F49, using
- net defined by OOA [i] based on linear OOA(4933, 300, F49, 17, 17) (dual of [(300, 17), 5067, 18]-NRT-code), using
- OOA 8-folding and stacking with additional row [i] based on linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using
- an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- OOA 8-folding and stacking with additional row [i] based on linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using
- net defined by OOA [i] based on linear OOA(4933, 300, F49, 17, 17) (dual of [(300, 17), 5067, 18]-NRT-code), using
- digital (1, 9, 51)-net over F49, using
(25, 42, 3893)-Net over F49 — Digital
Digital (25, 42, 3893)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4942, 3893, F49, 17) (dual of [3893, 3851, 18]-code), using
- 1481 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 16 times 0, 1, 59 times 0, 1, 185 times 0, 1, 446 times 0, 1, 766 times 0) [i] based on linear OA(4933, 2403, F49, 17) (dual of [2403, 2370, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(4933, 2401, F49, 17) (dual of [2401, 2368, 18]-code), using an extension Ce(16) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4931, 2401, F49, 16) (dual of [2401, 2370, 17]-code), using an extension Ce(15) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 16 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- 1481 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 0, 1, 16 times 0, 1, 59 times 0, 1, 185 times 0, 1, 446 times 0, 1, 766 times 0) [i] based on linear OA(4933, 2403, F49, 17) (dual of [2403, 2370, 18]-code), using
(25, 42, large)-Net in Base 49 — Upper bound on s
There is no (25, 42, large)-net in base 49, because
- 15 times m-reduction [i] would yield (25, 27, large)-net in base 49, but