Best Known (30, 62, s)-Nets in Base 32
(30, 62, 196)-Net over F32 — Constructive and digital
Digital (30, 62, 196)-net over F32, using
- (u, u+v)-construction [i] based on
- digital (7, 23, 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, 39, 98)-net over F32, using
- net from sequence [i] based on digital (7, 97)-sequence over F32 (see above)
- digital (7, 23, 98)-net over F32, using
(30, 62, 288)-Net in Base 32 — Constructive
(30, 62, 288)-net in base 32, using
- 10 times m-reduction [i] based on (30, 72, 288)-net in base 32, using
- base change [i] based on (18, 60, 288)-net in base 64, using
- 3 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on digital (9, 54, 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, 54, 288)-net over F128, using
- 3 times m-reduction [i] based on (18, 63, 288)-net in base 64, using
- base change [i] based on (18, 60, 288)-net in base 64, using
(30, 62, 475)-Net over F32 — Digital
Digital (30, 62, 475)-net over F32, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OOA(3262, 475, F32, 2, 32) (dual of [(475, 2), 888, 33]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3262, 511, F32, 2, 32) (dual of [(511, 2), 960, 33]-NRT-code), using
- OOA 2-folding [i] based on linear OA(3262, 1022, F32, 32) (dual of [1022, 960, 33]-code), using
- discarding factors / shortening the dual code based on linear OA(3262, 1023, F32, 32) (dual of [1023, 961, 33]-code), using
- 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]
- discarding factors / shortening the dual code based on linear OA(3262, 1023, F32, 32) (dual of [1023, 961, 33]-code), using
- OOA 2-folding [i] based on linear OA(3262, 1022, F32, 32) (dual of [1022, 960, 33]-code), using
- discarding factors / shortening the dual code based on linear OOA(3262, 511, F32, 2, 32) (dual of [(511, 2), 960, 33]-NRT-code), using
(30, 62, 149145)-Net in Base 32 — Upper bound on s
There is no (30, 62, 149146)-net in base 32, because
- the generalized Rao bound for nets shows that 32m ≥ 2086 059685 247336 101707 795058 001211 362153 845752 825356 718520 542360 717972 230541 672048 938739 068807 > 3262 [i]