Best Known (30, 64, s)-Nets in Base 25
(30, 64, 204)-Net over F25 — Constructive and digital
Digital (30, 64, 204)-net over F25, using
- net from sequence [i] based on digital (30, 203)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 30 and N(F) ≥ 204, using
(30, 64, 308)-Net over F25 — Digital
Digital (30, 64, 308)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2564, 308, F25, 2, 34) (dual of [(308, 2), 552, 35]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2564, 314, F25, 2, 34) (dual of [(314, 2), 564, 35]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2564, 628, F25, 34) (dual of [628, 564, 35]-code), using
- construction XX applied to C1 = C([623,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([623,32]) [i] based on
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,31}, and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2562, 624, F25, 33) (dual of [624, 562, 34]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,32], and designed minimum distance d ≥ |I|+1 = 34 [i]
- linear OA(2564, 624, F25, 34) (dual of [624, 560, 35]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,32}, and designed minimum distance d ≥ |I|+1 = 35 [i]
- linear OA(2560, 624, F25, 32) (dual of [624, 564, 33]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,31], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(250, s, F25, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- linear OA(250, 2, F25, 0) (dual of [2, 2, 1]-code) (see above)
- construction XX applied to C1 = C([623,31]), C2 = C([0,32]), C3 = C1 + C2 = C([0,31]), and C∩ = C1 ∩ C2 = C([623,32]) [i] based on
- OOA 2-folding [i] based on linear OA(2564, 628, F25, 34) (dual of [628, 564, 35]-code), using
- discarding factors / shortening the dual code based on linear OOA(2564, 314, F25, 2, 34) (dual of [(314, 2), 564, 35]-NRT-code), using
(30, 64, 54764)-Net in Base 25 — Upper bound on s
There is no (30, 64, 54765)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 293933 450424 054909 611023 015952 478774 088352 675565 899694 083960 541764 285477 108998 185073 207225 > 2564 [i]