Best Known (19, 19+21, s)-Nets in Base 25
(19, 19+21, 148)-Net over F25 — Constructive and digital
Digital (19, 40, 148)-net over F25, using
- net from sequence [i] based on digital (19, 147)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 19 and N(F) ≥ 148, using
(19, 19+21, 237)-Net over F25 — Digital
Digital (19, 40, 237)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2540, 237, F25, 21) (dual of [237, 197, 22]-code), using
- discarding factors / shortening the dual code based on linear OA(2540, 312, F25, 21) (dual of [312, 272, 22]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 312 | 252−1, defining interval I = [0,20], and designed minimum distance d ≥ |I|+1 = 22 [i]
- discarding factors / shortening the dual code based on linear OA(2540, 312, F25, 21) (dual of [312, 272, 22]-code), using
(19, 19+21, 53418)-Net in Base 25 — Upper bound on s
There is no (19, 40, 53419)-net in base 25, because
- 1 times m-reduction [i] would yield (19, 39, 53419)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 3 309075 055026 574220 742176 533964 733300 811807 313217 550033 > 2539 [i]