Best Known (29, 29+12, s)-Nets in Base 4
(29, 29+12, 240)-Net over F4 — Constructive and digital
Digital (29, 41, 240)-net over F4, using
- 1 times m-reduction [i] based on digital (29, 42, 240)-net over F4, using
- trace code for nets [i] based on digital (1, 14, 80)-net over F64, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 1 and N(F) ≥ 80, using
- net from sequence [i] based on digital (1, 79)-sequence over F64, using
- trace code for nets [i] based on digital (1, 14, 80)-net over F64, using
(29, 29+12, 305)-Net over F4 — Digital
Digital (29, 41, 305)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(441, 305, F4, 12) (dual of [305, 264, 13]-code), using
- 45 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 21 times 0) [i] based on linear OA(436, 255, F4, 12) (dual of [255, 219, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 255 = 44−1, defining interval I = [1,12], and designed minimum distance d ≥ |I|+1 = 13 [i]
- 45 step Varšamov–Edel lengthening with (ri) = (2, 0, 0, 1, 6 times 0, 1, 12 times 0, 1, 21 times 0) [i] based on linear OA(436, 255, F4, 12) (dual of [255, 219, 13]-code), using
(29, 29+12, 12972)-Net in Base 4 — Upper bound on s
There is no (29, 41, 12973)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 4 836610 690795 089579 555100 > 441 [i]