Best Known (50−26, 50, s)-Nets in Base 25
(50−26, 50, 153)-Net over F25 — Constructive and digital
Digital (24, 50, 153)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 14, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-sequence over F25, using
- digital (10, 36, 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 (1, 14, 27)-net over F25, using
(50−26, 50, 314)-Net over F25 — Digital
Digital (24, 50, 314)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2550, 314, F25, 2, 26) (dual of [(314, 2), 578, 27]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2550, 628, F25, 26) (dual of [628, 578, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(23) [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]
- linear OA(2547, 625, F25, 24) (dual of [625, 578, 25]-code), using an extension Ce(23) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,23], and designed minimum distance d ≥ |I|+1 = 24 [i]
- linear OA(251, 3, F25, 1) (dual of [3, 2, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(251, s, F25, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(23) [i] based on
- OOA 2-folding [i] based on linear OA(2550, 628, F25, 26) (dual of [628, 578, 27]-code), using
(50−26, 50, 56212)-Net in Base 25 — Upper bound on s
There is no (24, 50, 56213)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 7888 614182 801357 191039 438732 569973 292507 660392 723025 445137 901987 878425 > 2550 [i]