Best Known (34, 70, s)-Nets in Base 32
(34, 70, 202)-Net over F32 — Constructive and digital
Digital (34, 70, 202)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 25, 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 (9, 45, 104)-net over F32, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 9 and N(F) ≥ 104, using
- net from sequence [i] based on digital (9, 103)-sequence over F32, using
- digital (7, 25, 98)-net over F32, using
(34, 70, 288)-Net in Base 32 — Constructive
(34, 70, 288)-net in base 32, using
- t-expansion [i] based on (33, 70, 288)-net in base 32, using
- 14 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
- 14 times m-reduction [i] based on (33, 84, 288)-net in base 32, using
(34, 70, 515)-Net over F32 — Digital
Digital (34, 70, 515)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3270, 515, F32, 2, 36) (dual of [(515, 2), 960, 37]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3270, 1030, F32, 36) (dual of [1030, 960, 37]-code), using
- discarding factors / shortening the dual code based on linear OA(3270, 1031, F32, 36) (dual of [1031, 961, 37]-code), using
- construction X applied to Ce(35) ⊂ Ce(32) [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(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(322, 7, F32, 2) (dual of [7, 5, 3]-code or 7-arc in PG(1,32)), using
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- Reed–Solomon code RS(30,32) [i]
- discarding factors / shortening the dual code based on linear OA(322, 32, F32, 2) (dual of [32, 30, 3]-code or 32-arc in PG(1,32)), using
- construction X applied to Ce(35) ⊂ Ce(32) [i] based on
- discarding factors / shortening the dual code based on linear OA(3270, 1031, F32, 36) (dual of [1031, 961, 37]-code), using
- OOA 2-folding [i] based on linear OA(3270, 1030, F32, 36) (dual of [1030, 960, 37]-code), using
(34, 70, 173822)-Net in Base 32 — Upper bound on s
There is no (34, 70, 173823)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2293 549803 115021 678572 254882 054988 056667 584455 531215 285938 458468 581124 767724 877940 835980 824717 038480 513123 > 3270 [i]