Best Known (33−18, 33, s)-Nets in Base 25
(33−18, 33, 126)-Net over F25 — Constructive and digital
Digital (15, 33, 126)-net over F25, using
- t-expansion [i] based on digital (10, 33, 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
(33−18, 33, 171)-Net over F25 — Digital
Digital (15, 33, 171)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2533, 171, F25, 18) (dual of [171, 138, 19]-code), using
- discarding factors / shortening the dual code based on linear OA(2533, 208, F25, 18) (dual of [208, 175, 19]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 208 | 252−1, defining interval I = [0,17], and designed minimum distance d ≥ |I|+1 = 19 [i]
- discarding factors / shortening the dual code based on linear OA(2533, 208, F25, 18) (dual of [208, 175, 19]-code), using
(33−18, 33, 23080)-Net in Base 25 — Upper bound on s
There is no (15, 33, 23081)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 13557 215810 955896 264361 422195 446616 782486 550425 > 2533 [i]