Best Known (29, 29+26, s)-Nets in Base 25
(29, 29+26, 200)-Net over F25 — Constructive and digital
Digital (29, 55, 200)-net over F25, using
- t-expansion [i] based on digital (25, 55, 200)-net over F25, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 25 and N(F) ≥ 200, using
- net from sequence [i] based on digital (25, 199)-sequence over F25, using
(29, 29+26, 560)-Net over F25 — Digital
Digital (29, 55, 560)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(2555, 560, F25, 26) (dual of [560, 505, 27]-code), using
- discarding factors / shortening the dual code based on linear OA(2555, 643, F25, 26) (dual of [643, 588, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(18) [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(2537, 625, F25, 19) (dual of [625, 588, 20]-code), using an extension Ce(18) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,18], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(256, 18, F25, 6) (dual of [18, 12, 7]-code or 18-arc in PG(5,25)), using
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- Reed–Solomon code RS(19,25) [i]
- discarding factors / shortening the dual code based on linear OA(256, 25, F25, 6) (dual of [25, 19, 7]-code or 25-arc in PG(5,25)), using
- construction X applied to Ce(25) ⊂ Ce(18) [i] based on
- discarding factors / shortening the dual code based on linear OA(2555, 643, F25, 26) (dual of [643, 588, 27]-code), using
(29, 29+26, 193883)-Net in Base 25 — Upper bound on s
There is no (29, 55, 193884)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 77037 456457 274713 549032 813683 658343 097010 358927 788004 815337 453126 908552 539425 > 2555 [i]