Best Known (16, 16+19, s)-Nets in Base 25
(16, 16+19, 126)-Net over F25 — Constructive and digital
Digital (16, 35, 126)-net over F25, using
- t-expansion [i] based on digital (10, 35, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(16, 16+19, 180)-Net over F25 — Digital
Digital (16, 35, 180)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2535, 180, F25, 19) (dual of [180, 145, 20]-code), using
- discarding factors / shortening the dual code based on linear OA(2535, 208, F25, 19) (dual of [208, 173, 20]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 208 | 252−1, defining interval I = [0,18], and designed minimum distance d ≥ |I|+1 = 20 [i]
- discarding factors / shortening the dual code based on linear OA(2535, 208, F25, 19) (dual of [208, 173, 20]-code), using
(16, 16+19, 33005)-Net in Base 25 — Upper bound on s
There is no (16, 35, 33006)-net in base 25, because
- 1 times m-reduction [i] would yield (16, 34, 33006)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 338838 106943 126610 361780 102798 632967 463968 092625 > 2534 [i]