Best Known (100−48, 100, s)-Nets in Base 32
(100−48, 100, 240)-Net over F32 — Constructive and digital
Digital (52, 100, 240)-net over F32, using
- t-expansion [i] based on digital (51, 100, 240)-net over F32, using
- 9 times m-reduction [i] based on digital (51, 109, 240)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (11, 40, 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, 69, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32 (see above)
- digital (11, 40, 120)-net over F32, using
- (u, u+v)-construction [i] based on
- 9 times m-reduction [i] based on digital (51, 109, 240)-net over F32, using
(100−48, 100, 513)-Net in Base 32 — Constructive
(52, 100, 513)-net in base 32, using
- t-expansion [i] based on (46, 100, 513)-net in base 32, using
- 8 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
- 8 times m-reduction [i] based on (46, 108, 513)-net in base 32, using
(100−48, 100, 986)-Net over F32 — Digital
Digital (52, 100, 986)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(32100, 986, F32, 48) (dual of [986, 886, 49]-code), using
- discarding factors / shortening the dual code based on linear OA(32100, 1050, F32, 48) (dual of [1050, 950, 49]-code), using
- construction X applied to Ce(47) ⊂ Ce(38) [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(3274, 1024, F32, 39) (dual of [1024, 950, 40]-code), using an extension Ce(38) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,38], and designed minimum distance d ≥ |I|+1 = 39 [i]
- linear OA(328, 26, F32, 8) (dual of [26, 18, 9]-code or 26-arc in PG(7,32)), using
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
- Reed–Solomon code RS(24,32) [i]
- discarding factors / shortening the dual code based on linear OA(328, 32, F32, 8) (dual of [32, 24, 9]-code or 32-arc in PG(7,32)), using
- construction X applied to Ce(47) ⊂ Ce(38) [i] based on
- discarding factors / shortening the dual code based on linear OA(32100, 1050, F32, 48) (dual of [1050, 950, 49]-code), using
(100−48, 100, 590813)-Net in Base 32 — Upper bound on s
There is no (52, 100, 590814)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 3 273483 731992 338137 349328 924184 942372 902809 971619 801483 909568 063501 710476 526525 866536 245179 500907 382647 396738 843911 060939 051663 025555 250123 140005 133863 > 32100 [i]