Best Known (25, 25+28, s)-Nets in Base 25
(25, 25+28, 200)-Net over F25 — Constructive and digital
Digital (25, 53, 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
(25, 25+28, 289)-Net over F25 — Digital
Digital (25, 53, 289)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2553, 289, F25, 2, 28) (dual of [(289, 2), 525, 29]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2553, 314, F25, 2, 28) (dual of [(314, 2), 575, 29]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2553, 628, F25, 28) (dual of [628, 575, 29]-code), using
- discarding factors / shortening the dual code based on linear OA(2553, 629, F25, 28) (dual of [629, 576, 29]-code), using
- construction X applied to Ce(27) ⊂ Ce(25) [i] based on
- linear OA(2552, 625, F25, 28) (dual of [625, 573, 29]-code), using an extension Ce(27) of the primitive narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [1,27], and designed minimum distance d ≥ |I|+1 = 28 [i]
- 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(251, 4, F25, 1) (dual of [4, 3, 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(27) ⊂ Ce(25) [i] based on
- discarding factors / shortening the dual code based on linear OA(2553, 629, F25, 28) (dual of [629, 576, 29]-code), using
- OOA 2-folding [i] based on linear OA(2553, 628, F25, 28) (dual of [628, 575, 29]-code), using
- discarding factors / shortening the dual code based on linear OOA(2553, 314, F25, 2, 28) (dual of [(314, 2), 575, 29]-NRT-code), using
(25, 25+28, 49361)-Net in Base 25 — Upper bound on s
There is no (25, 53, 49362)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 123 287739 685708 041393 442977 029041 422568 630534 702545 923288 175387 755032 211425 > 2553 [i]