Best Known (76−38, 76, s)-Nets in Base 32
(76−38, 76, 218)-Net over F32 — Constructive and digital
Digital (38, 76, 218)-net over F32, using
- 2 times m-reduction [i] based on digital (38, 78, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 27, 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, 51, 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, 27, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(76−38, 76, 288)-Net in Base 32 — Constructive
(38, 76, 288)-net in base 32, using
- t-expansion [i] based on (37, 76, 288)-net in base 32, using
- 22 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
- base change [i] based on digital (9, 70, 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, 70, 288)-net over F128, using
- 22 times m-reduction [i] based on (37, 98, 288)-net in base 32, using
(76−38, 76, 613)-Net over F32 — Digital
Digital (38, 76, 613)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3276, 613, F32, 38) (dual of [613, 537, 39]-code), using
- discarding factors / shortening the dual code based on linear OA(3276, 1037, F32, 38) (dual of [1037, 961, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- linear OA(3272, 1024, F32, 38) (dual of [1024, 952, 39]-code), using an extension Ce(37) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,37], and designed minimum distance d ≥ |I|+1 = 38 [i]
- linear OA(3263, 1024, F32, 33) (dual of [1024, 961, 34]-code), using an extension Ce(32) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,32], and designed minimum distance d ≥ |I|+1 = 33 [i]
- linear OA(324, 13, F32, 4) (dual of [13, 9, 5]-code or 13-arc in PG(3,32)), using
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- Reed–Solomon code RS(28,32) [i]
- discarding factors / shortening the dual code based on linear OA(324, 32, F32, 4) (dual of [32, 28, 5]-code or 32-arc in PG(3,32)), using
- construction X applied to Ce(37) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(3276, 1037, F32, 38) (dual of [1037, 961, 39]-code), using
(76−38, 76, 268187)-Net in Base 32 — Upper bound on s
There is no (38, 76, 268188)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 462752 751426 789051 725871 001598 727656 596398 836204 286505 721166 047199 098166 796986 205234 237185 634545 653058 742986 494717 > 3276 [i]