Best Known (48−25, 48, s)-Nets in Base 25
(48−25, 48, 153)-Net over F25 — Constructive and digital
Digital (23, 48, 153)-net over F25, using
- (u, u+v)-construction [i] based on
- digital (1, 13, 27)-net over F25, using
- net from sequence [i] based on digital (1, 26)-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 (1, 13, 27)-net over F25, using
(48−25, 48, 305)-Net over F25 — Digital
Digital (23, 48, 305)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2548, 305, F25, 2, 25) (dual of [(305, 2), 562, 26]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2548, 312, F25, 2, 25) (dual of [(312, 2), 576, 26]-NRT-code), using
- OOA 2-folding [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]
- OOA 2-folding [i] based on linear OA(2548, 624, F25, 25) (dual of [624, 576, 26]-code), using
- discarding factors / shortening the dual code based on linear OOA(2548, 312, F25, 2, 25) (dual of [(312, 2), 576, 26]-NRT-code), using
(48−25, 48, 65822)-Net in Base 25 — Upper bound on s
There is no (23, 48, 65823)-net in base 25, because
- 1 times m-reduction [i] would yield (23, 47, 65823)-net in base 25, but
- the generalized Rao bound for nets shows that 25m ≥ 504899 592061 112951 375285 532380 895110 421735 005796 705806 551177 018081 > 2547 [i]