Best Known (33, 70, s)-Nets in Base 32
(33, 70, 196)-Net over F32 — Constructive and digital
Digital (33, 70, 196)-net over F32, using
- 1 times m-reduction [i] based on digital (33, 71, 196)-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 (7, 45, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 26, 98)-net over F32, using
- (u, u+v)-construction [i] based on
(33, 70, 288)-Net in Base 32 — Constructive
(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
(33, 70, 430)-Net over F32 — Digital
Digital (33, 70, 430)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3270, 430, F32, 2, 37) (dual of [(430, 2), 790, 38]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3270, 513, F32, 2, 37) (dual of [(513, 2), 956, 38]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3270, 1026, F32, 37) (dual of [1026, 956, 38]-code), using
- construction X applied to Ce(36) ⊂ Ce(35) [i] based on
- 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(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(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(36) ⊂ Ce(35) [i] based on
- OOA 2-folding [i] based on linear OA(3270, 1026, F32, 37) (dual of [1026, 956, 38]-code), using
- discarding factors / shortening the dual code based on linear OOA(3270, 513, F32, 2, 37) (dual of [(513, 2), 956, 38]-NRT-code), using
(33, 70, 143377)-Net in Base 32 — Upper bound on s
There is no (33, 70, 143378)-net in base 32, because
- 1 times m-reduction [i] would yield (33, 69, 143378)-net in base 32, but
- the generalized Rao bound for nets shows that 32m ≥ 71 672056 981533 576291 191435 760307 191068 465322 620514 036687 363903 244202 830738 477577 548065 589545 935108 407744 > 3269 [i]