Best Known (13, 30, s)-Nets in Base 49
(13, 30, 150)-Net over F49 — Constructive and digital
Digital (13, 30, 150)-net over F49, using
- generalized (u, u+v)-construction [i] based on
- digital (0, 5, 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, 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)
- digital (0, 5, 50)-net over F49, using
(13, 30, 242)-Net over F49 — Digital
Digital (13, 30, 242)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4930, 242, F49, 17) (dual of [242, 212, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(4930, 243, F49, 17) (dual of [243, 213, 18]-code), using
- construction X applied to Ce(16) ⊂ Ce(15) [i] based on
- linear OA(4930, 241, F49, 17) (dual of [241, 211, 18]-code), using an extension Ce(16) of the narrow-sense BCH-code C(I) with length 240 | 492−1, defining interval I = [1,16], and designed minimum distance d ≥ |I|+1 = 17 [i]
- linear OA(4928, 241, F49, 16) (dual of [241, 213, 17]-code), using an extension Ce(15) of the narrow-sense BCH-code C(I) with length 240 | 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
- discarding factors / shortening the dual code based on linear OA(4930, 243, F49, 17) (dual of [243, 213, 18]-code), using
(13, 30, 105049)-Net in Base 49 — Upper bound on s
There is no (13, 30, 105050)-net in base 49, because
- 1 times m-reduction [i] would yield (13, 29, 105050)-net in base 49, but
- the generalized Rao bound for nets shows that 49m ≥ 10 368098 043206 924914 124103 330988 941559 131130 202881 > 4929 [i]