Best Known (39, 39+40, s)-Nets in Base 32
(39, 39+40, 218)-Net over F32 — Constructive and digital
Digital (39, 79, 218)-net over F32, using
- 2 times m-reduction [i] based on digital (39, 81, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 28, 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 (11, 53, 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 (7, 28, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(39, 39+40, 288)-Net in Base 32 — Constructive
(39, 79, 288)-net in base 32, using
- 26 times m-reduction [i] based on (39, 105, 288)-net in base 32, using
- base change [i] based on digital (9, 75, 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, 75, 288)-net over F128, using
(39, 39+40, 579)-Net over F32 — Digital
Digital (39, 79, 579)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3279, 579, F32, 40) (dual of [579, 500, 41]-code), using
- discarding factors / shortening the dual code based on linear OA(3279, 1035, F32, 40) (dual of [1035, 956, 41]-code), using
- construction X applied to Ce(39) ⊂ Ce(35) [i] based on
- linear OA(3276, 1024, F32, 40) (dual of [1024, 948, 41]-code), using an extension Ce(39) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,39], and designed minimum distance d ≥ |I|+1 = 40 [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(323, 11, F32, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,32) or 11-cap in PG(2,32)), using
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- Reed–Solomon code RS(29,32) [i]
- discarding factors / shortening the dual code based on linear OA(323, 32, F32, 3) (dual of [32, 29, 4]-code or 32-arc in PG(2,32) or 32-cap in PG(2,32)), using
- construction X applied to Ce(39) ⊂ Ce(35) [i] based on
- discarding factors / shortening the dual code based on linear OA(3279, 1035, F32, 40) (dual of [1035, 956, 41]-code), using
(39, 39+40, 236193)-Net in Base 32 — Upper bound on s
There is no (39, 79, 236194)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 80697 401855 215511 511014 654712 808782 744809 823041 655268 128045 872621 171875 540544 031290 655135 131834 147182 490656 694229 652552 > 3279 [i]