Best Known (51, 97, s)-Nets in Base 32
(51, 97, 240)-Net over F32 — Constructive and digital
Digital (51, 97, 240)-net over F32, using
- 12 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
(51, 97, 513)-Net in Base 32 — Constructive
(51, 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
(51, 97, 1050)-Net over F32 — Digital
Digital (51, 97, 1050)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3297, 1050, F32, 46) (dual of [1050, 953, 47]-code), using
- discarding factors / shortening the dual code based on linear OA(3297, 1053, F32, 46) (dual of [1053, 956, 47]-code), using
- construction X applied to Ce(45) ⊂ Ce(35) [i] based on
- linear OA(3288, 1024, F32, 46) (dual of [1024, 936, 47]-code), using an extension Ce(45) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,45], and designed minimum distance d ≥ |I|+1 = 46 [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(329, 29, F32, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,32)), using
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- Reed–Solomon code RS(23,32) [i]
- discarding factors / shortening the dual code based on linear OA(329, 32, F32, 9) (dual of [32, 23, 10]-code or 32-arc in PG(8,32)), using
- construction X applied to Ce(45) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(3297, 1053, F32, 46) (dual of [1053, 956, 47]-code), using
(51, 97, 677475)-Net in Base 32 — Upper bound on s
There is no (51, 97, 677476)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 99 898206 041866 388333 576538 265117 316099 808906 243384 808682 279055 592454 041897 816855 795740 862715 240067 151629 139778 354027 916412 895322 610518 811843 700888 > 3297 [i]