Best Known (61−32, 61, s)-Nets in Base 25
(61−32, 61, 200)-Net over F25 — Constructive and digital
Digital (29, 61, 200)-net over F25, using
- t-expansion [i] based on digital (25, 61, 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
(61−32, 61, 315)-Net over F25 — Digital
Digital (29, 61, 315)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2561, 315, F25, 2, 32) (dual of [(315, 2), 569, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2561, 630, F25, 32) (dual of [630, 569, 33]-code), using
- construction X applied to Ce(31) ⊂ Ce(29) [i] based on
- linear OA(2560, 625, F25, 32) (dual of [625, 565, 33]-code), using an extension Ce(31) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,31], and designed minimum distance d ≥ |I|+1 = 32 [i]
- linear OA(2556, 625, F25, 30) (dual of [625, 569, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(251, 5, F25, 1) (dual of [5, 4, 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(31) ⊂ Ce(29) [i] based on
- OOA 2-folding [i] based on linear OA(2561, 630, F25, 32) (dual of [630, 569, 33]-code), using
(61−32, 61, 60522)-Net in Base 25 — Upper bound on s
There is no (29, 61, 60523)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 18 811566 218913 991830 294663 655146 671809 088256 935783 406806 367041 671429 254218 427089 296513 > 2561 [i]