Best Known (25, 25+25, s)-Nets in Base 32
(25, 25+25, 174)-Net over F32 — Constructive and digital
Digital (25, 50, 174)-net over F32, using
- 1 times m-reduction [i] based on digital (25, 51, 174)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (5, 18, 76)-net over F32, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 5 and N(F) ≥ 76, using
- net from sequence [i] based on digital (5, 75)-sequence over F32, using
- digital (7, 33, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 7 and N(F) ≥ 98, using
- net from sequence [i] based on digital (7, 97)-sequence over F32, using
- digital (5, 18, 76)-net over F32, using
- (u, u+v)-construction [i] based on
(25, 25+25, 288)-Net in Base 32 — Constructive
(25, 50, 288)-net in base 32, using
- 6 times m-reduction [i] based on (25, 56, 288)-net in base 32, using
- base change [i] based on digital (9, 40, 288)-net over F128, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 9 and N(F) ≥ 288, using
- net from sequence [i] based on digital (9, 287)-sequence over F128, using
- base change [i] based on digital (9, 40, 288)-net over F128, using
(25, 25+25, 515)-Net over F32 — Digital
Digital (25, 50, 515)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3250, 515, F32, 2, 25) (dual of [(515, 2), 980, 26]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3250, 1030, F32, 25) (dual of [1030, 980, 26]-code), using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- linear OA(3249, 1025, F32, 25) (dual of [1025, 976, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,12], and minimum distance d ≥ |{−12,−11,…,12}|+1 = 26 (BCH-bound) [i]
- linear OA(3245, 1025, F32, 23) (dual of [1025, 980, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 1025 | 324−1, defining interval I = [0,11], and minimum distance d ≥ |{−11,−10,…,11}|+1 = 24 (BCH-bound) [i]
- linear OA(321, 5, F32, 1) (dual of [5, 4, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(321, s, F32, 1) (dual of [s, s−1, 2]-code) with arbitrarily large s, using
- construction X applied to C([0,12]) ⊂ C([0,11]) [i] based on
- OOA 2-folding [i] based on linear OA(3250, 1030, F32, 25) (dual of [1030, 980, 26]-code), using
(25, 25+25, 238791)-Net in Base 32 — Upper bound on s
There is no (25, 50, 238792)-net in base 32, because
- 1 times m-reduction [i] would yield (25, 49, 238792)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 56 541733 435692 859781 145113 951073 086822 385027 532869 223605 297809 936206 496232 > 3249 [i]