Best Known (31, 56, s)-Nets in Base 25
(31, 56, 230)-Net over F25 — Constructive and digital
Digital (31, 56, 230)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 21, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F25, using
- 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
- digital (9, 21, 104)-net over F25, using
(31, 56, 769)-Net over F25 — Digital
Digital (31, 56, 769)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2556, 769, F25, 25) (dual of [769, 713, 26]-code), using
- 137 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 6 times 0, 1, 18 times 0, 1, 38 times 0, 1, 68 times 0) [i] based on linear OA(2548, 624, F25, 25) (dual of [624, 576, 26]-code), using
- the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- 137 step Varšamov–Edel lengthening with (ri) = (4, 0, 0, 1, 6 times 0, 1, 18 times 0, 1, 38 times 0, 1, 68 times 0) [i] based on linear OA(2548, 624, F25, 25) (dual of [624, 576, 26]-code), using
(31, 56, 562821)-Net in Base 25 — Upper bound on s
There is no (31, 56, 562822)-net in base 25, because
- 1 times m-reduction [i] would yield (31, 55, 562822)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 77038 226319 186768 302456 638304 811110 476693 551160 361488 443821 462695 043895 952705 > 2555 [i]