Best Known (43, 43+42, s)-Nets in Base 32
(43, 43+42, 240)-Net over F32 — Constructive and digital
Digital (43, 85, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 32, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- digital (11, 53, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 32, 120)-net over F32, using
(43, 43+42, 513)-Net in Base 32 — Constructive
(43, 85, 513)-net in base 32, using
- 5 times m-reduction [i] based on (43, 90, 513)-net in base 32, using
- base change [i] based on digital (28, 75, 513)-net over F64, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- the Hermitian function field over F64 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 28 and N(F) ≥ 513, using
- net from sequence [i] based on digital (28, 512)-sequence over F64, using
- base change [i] based on digital (28, 75, 513)-net over F64, using
(43, 43+42, 718)-Net over F32 — Digital
Digital (43, 85, 718)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3285, 718, F32, 42) (dual of [718, 633, 43]-code), using
- discarding factors / shortening the dual code based on linear OA(3285, 1041, F32, 42) (dual of [1041, 956, 43]-code), using
- construction X applied to Ce(41) ⊂ Ce(35) [i] based on
- linear OA(3280, 1024, F32, 42) (dual of [1024, 944, 43]-code), using an extension Ce(41) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,41], and designed minimum distance d ≥ |I|+1 = 42 [i]
- linear OA(3268, 1024, F32, 36) (dual of [1024, 956, 37]-code), using an extension Ce(35) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,35], and designed minimum distance d ≥ |I|+1 = 36 [i]
- linear OA(325, 17, F32, 5) (dual of [17, 12, 6]-code or 17-arc in PG(4,32)), using
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- Reed–Solomon code RS(27,32) [i]
- discarding factors / shortening the dual code based on linear OA(325, 32, F32, 5) (dual of [32, 27, 6]-code or 32-arc in PG(4,32)), using
- construction X applied to Ce(41) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(3285, 1041, F32, 42) (dual of [1041, 956, 43]-code), using
(43, 43+42, 346251)-Net in Base 32 — Upper bound on s
There is no (43, 85, 346252)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 86 650484 647066 069421 397684 957516 530886 024130 287933 669977 060311 416047 903941 562882 596395 546280 107569 672626 676459 024217 320937 389808 > 3285 [i]