Best Known (97−48, 97, s)-Nets in Base 32
(97−48, 97, 240)-Net over F32 — Constructive and digital
Digital (49, 97, 240)-net over F32, using
- 6 times m-reduction [i] based on digital (49, 103, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 38, 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, 65, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 38, 120)-net over F32, using
- (u, u+v)-construction [i] based on
(97−48, 97, 513)-Net in Base 32 — Constructive
(49, 97, 513)-net in base 32, using
- t-expansion [i] based on (46, 97, 513)-net in base 32, using
- 11 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
- base change [i] based on digital (28, 90, 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, 90, 513)-net over F64, using
- 11 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(97−48, 97, 783)-Net over F32 — Digital
Digital (49, 97, 783)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3297, 783, F32, 48) (dual of [783, 686, 49]-code), using
- discarding factors / shortening the dual code based on linear OA(3297, 1041, F32, 48) (dual of [1041, 944, 49]-code), using
- construction X applied to Ce(47) ⊂ Ce(41) [i] based on
- linear OA(3292, 1024, F32, 48) (dual of [1024, 932, 49]-code), using an extension Ce(47) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,47], and designed minimum distance d ≥ |I|+1 = 48 [i]
- 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(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(47) ⊂ Ce(41) [i] based on
- discarding factors / shortening the dual code based on linear OA(3297, 1041, F32, 48) (dual of [1041, 944, 49]-code), using
(97−48, 97, 383090)-Net in Base 32 — Upper bound on s
There is no (49, 97, 383091)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 99 897750 358099 644840 068246 392615 480068 233963 652228 131739 402928 883599 412422 012194 622304 534838 489139 219177 057005 944718 027020 836751 838067 861075 414132 > 3297 [i]