Best Known (57−26, 57, s)-Nets in Base 25
(57−26, 57, 208)-Net over F25 — Constructive and digital
Digital (31, 57, 208)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (9, 22, 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 (9, 35, 104)-net over F25, using
- net from sequence [i] based on digital (9, 103)-sequence over F25 (see above)
- digital (9, 22, 104)-net over F25, using
(57−26, 57, 700)-Net over F25 — Digital
Digital (31, 57, 700)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2557, 700, F25, 26) (dual of [700, 643, 27]-code), using
- 67 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 36 times 0) [i] based on linear OA(2549, 625, F25, 26) (dual of [625, 576, 27]-code), using
- an extension Ce(25) of 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]
- 67 step Varšamov–Edel lengthening with (ri) = (4, 1, 0, 0, 1, 7 times 0, 1, 17 times 0, 1, 36 times 0) [i] based on linear OA(2549, 625, F25, 26) (dual of [625, 576, 27]-code), using
(57−26, 57, 318137)-Net in Base 25 — Upper bound on s
There is no (31, 57, 318138)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 48 148639 529271 981654 051776 779590 929766 422563 957346 868600 112080 809965 515730 987825 > 2557 [i]