Best Known (73−36, 73, s)-Nets in Base 32
(73−36, 73, 218)-Net over F32 — Constructive and digital
Digital (37, 73, 218)-net over F32, using
- 2 times m-reduction [i] based on digital (37, 75, 218)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 26, 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, 49, 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, 26, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(73−36, 73, 288)-Net in Base 32 — Constructive
(37, 73, 288)-net in base 32, using
- 25 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
(73−36, 73, 657)-Net over F32 — Digital
Digital (37, 73, 657)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(3273, 657, F32, 36) (dual of [657, 584, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3273, 1038, F32, 36) (dual of [1038, 965, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(29) [i] based on
- 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(3259, 1024, F32, 30) (dual of [1024, 965, 31]-code), using an extension Ce(29) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,29], and designed minimum distance d ≥ |I|+1 = 30 [i]
- linear OA(325, 14, F32, 5) (dual of [14, 9, 6]-code or 14-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(35) ⊂ Ce(29) [i] based on
- discarding factors / shortening the dual code based on linear OA(3273, 1038, F32, 36) (dual of [1038, 965, 37]-code), using
(73−36, 73, 309724)-Net in Base 32 — Upper bound on s
There is no (37, 73, 309725)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 75 157333 573999 501783 522272 784704 353427 266593 456217 092123 750216 868321 557468 432810 539719 135576 177983 237931 114206 > 3273 [i]