Best Known (26, 26+17, s)-Nets in Base 49
(26, 26+17, 400)-Net over F49 — Constructive and digital
Digital (26, 43, 400)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 2, 50)-net over F49, using
- digital (0, 2, 50)-net over F49 (see above)
- digital (0, 2, 50)-net over F49 (see above)
- digital (0, 3, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 0 and N(F) ≥ 50, using
- the rational function field F49(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 49)-sequence over F49, using
- digital (0, 4, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 5, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 8, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
- digital (0, 17, 50)-net over F49, using
- net from sequence [i] based on digital (0, 49)-sequence over F49 (see above)
(26, 26+17, 4949)-Net over F49 — Digital
Digital (26, 43, 4949)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4943, 4949, F49, 17) (dual of [4949, 4906, 18]-code), using
- 2536 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, 1, 1054 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
- 2536 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, 1, 1054 times 0) [i] based on linear OA(4933, 2403, F49, 17) (dual of [2403, 2370, 18]-code), using
(26, 26+17, large)-Net in Base 49 — Upper bound on s
There is no (26, 43, large)-net in base 49, because
- 15 times m-reduction [i] would yield (26, 28, large)-net in base 49, but