Best Known (34, 72, s)-Nets in Base 32
(34, 72, 196)-Net over F32 — Constructive and digital
Digital (34, 72, 196)-net over F32, using
- 2 times m-reduction [i] based on digital (34, 74, 196)-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 (7, 47, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 27, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(34, 72, 288)-Net in Base 32 — Constructive
(34, 72, 288)-net in base 32, using
- t-expansion [i] based on (33, 72, 288)-net in base 32, using
- 12 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
- base change [i] based on digital (9, 60, 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, 60, 288)-net over F128, using
- 12 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
(34, 72, 442)-Net over F32 — Digital
Digital (34, 72, 442)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3272, 442, F32, 2, 38) (dual of [(442, 2), 812, 39]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3272, 513, F32, 2, 38) (dual of [(513, 2), 954, 39]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3272, 1026, F32, 38) (dual of [1026, 954, 39]-code), using
- construction X applied to Ce(37) ⊂ Ce(36) [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(3270, 1024, F32, 37) (dual of [1024, 954, 38]-code), using an extension Ce(36) of the primitive narrow-sense BCH-code C(I) with length 1023 = 322−1, defining interval I = [1,36], and designed minimum distance d ≥ |I|+1 = 37 [i]
- linear OA(320, 2, F32, 0) (dual of [2, 2, 1]-code), using
- discarding factors / shortening the dual code based on linear OA(320, s, F32, 0) (dual of [s, s, 1]-code) with arbitrarily large s, using
- construction X applied to Ce(37) ⊂ Ce(36) [i] based on
- OOA 2-folding [i] based on linear OA(3272, 1026, F32, 38) (dual of [1026, 954, 39]-code), using
- discarding factors / shortening the dual code based on linear OOA(3272, 513, F32, 2, 38) (dual of [(513, 2), 954, 39]-NRT-code), using
(34, 72, 129284)-Net in Base 32 — Upper bound on s
There is no (34, 72, 129285)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2 348581 990360 985413 184954 560494 102173 737779 695823 463806 959160 061741 818701 781933 776965 545541 938807 719365 917760 > 3272 [i]