Best Known (25, 25+26, s)-Nets in Base 49
(25, 25+26, 344)-Net over F49 — Constructive and digital
Digital (25, 51, 344)-net over F49, using
- t-expansion [i] based on digital (21, 51, 344)-net over F49, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- the Hermitian function field over F49 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F49 with g(F) = 21 and N(F) ≥ 344, using
- net from sequence [i] based on digital (21, 343)-sequence over F49, using
(25, 25+26, 801)-Net over F49 — Digital
Digital (25, 51, 801)-net over F49, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(4951, 801, F49, 3, 26) (dual of [(801, 3), 2352, 27]-NRT-code), using
- OOA 3-folding [i] based on linear OA(4951, 2403, F49, 26) (dual of [2403, 2352, 27]-code), using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- linear OA(4951, 2401, F49, 26) (dual of [2401, 2350, 27]-code), using an extension Ce(25) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,25], and designed minimum distance d ≥ |I|+1 = 26 [i]
- linear OA(4949, 2401, F49, 25) (dual of [2401, 2352, 26]-code), using an extension Ce(24) of the primitive narrow-sense BCH-code C(I) with length 2400 = 492−1, defining interval I = [1,24], and designed minimum distance d ≥ |I|+1 = 25 [i]
- linear OA(490, 2, F49, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(490, s, F49, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(25) ⊂ Ce(24) [i] based on
- OOA 3-folding [i] based on linear OA(4951, 2403, F49, 26) (dual of [2403, 2352, 27]-code), using
(25, 25+26, 504578)-Net in Base 49 — Upper bound on s
There is no (25, 51, 504579)-net in base 49, because
- the generalized Rao bound for nets shows that 49m ≥ 158 491204 778666 214647 020034 943855 812286 939665 707811 545022 364272 400953 949949 364898 040657 > 4951 [i]