Best Known (11, 11+12, s)-Nets in Base 25
(11, 11+12, 126)-Net over F25 — Constructive and digital
Digital (11, 23, 126)-net over F25, using
- t-expansion [i] based on digital (10, 23, 126)-net over F25, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- the Hermitian function field over F25 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F25 with g(F) = 10 and N(F) ≥ 126, using
- net from sequence [i] based on digital (10, 125)-sequence over F25, using
(11, 11+12, 312)-Net over F25 — Digital
Digital (11, 23, 312)-net over F25, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(2523, 312, F25, 2, 12) (dual of [(312, 2), 601, 13]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(2523, 314, F25, 2, 12) (dual of [(314, 2), 605, 13]-NRT-code), using
- OOA 2-folding [i] based on linear OA(2523, 628, F25, 12) (dual of [628, 605, 13]-code), using
- construction XX applied to C1 = C([623,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([623,10]) [i] based on
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,9}, and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2521, 624, F25, 11) (dual of [624, 603, 12]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,10], and designed minimum distance d ≥ |I|+1 = 12 [i]
- linear OA(2523, 624, F25, 12) (dual of [624, 601, 13]-code), using the primitive BCH-code C(I) with length 624 = 252−1, defining interval I = {−1,0,…,10}, and designed minimum distance d ≥ |I|+1 = 13 [i]
- linear OA(2519, 624, F25, 10) (dual of [624, 605, 11]-code), using the primitive expurgated narrow-sense BCH-code C(I) with length 624 = 252−1, defining interval I = [0,9], and designed minimum distance d ≥ |I|+1 = 11 [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([623,9]), C2 = C([0,10]), C3 = C1 + C2 = C([0,9]), and C∩ = C1 ∩ C2 = C([623,10]) [i] based on
- OOA 2-folding [i] based on linear OA(2523, 628, F25, 12) (dual of [628, 605, 13]-code), using
- discarding factors / shortening the dual code based on linear OOA(2523, 314, F25, 2, 12) (dual of [(314, 2), 605, 13]-NRT-code), using
(11, 11+12, 28493)-Net in Base 25 — Upper bound on s
There is no (11, 23, 28494)-net in base 25, because
- the generalized Rao bound for nets shows that 25m ≥ 142 136933 401184 563550 003437 906849 > 2523 [i]