Best Known (149, 190, s)-Nets in Base 4
(149, 190, 1052)-Net over F4 — Constructive and digital
Digital (149, 190, 1052)-net over F4, using
- 42 times duplication [i] based on digital (147, 188, 1052)-net over F4, using
- trace code for nets [i] based on digital (6, 47, 263)-net over F256, using
- net from sequence [i] based on digital (6, 262)-sequence over F256, using
- trace code for nets [i] based on digital (6, 47, 263)-net over F256, using
(149, 190, 4168)-Net over F4 — Digital
Digital (149, 190, 4168)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(4190, 4168, F4, 41) (dual of [4168, 3978, 42]-code), using
- 62 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
- the expurgated narrow-sense BCH-code C(I) with length 4097 | 412−1, defining interval I = [0,20], and minimum distance d ≥ |{−20,−19,…,20}|+1 = 42 (BCH-bound) [i]
- 62 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 9 times 0, 1, 15 times 0, 1, 23 times 0) [i] based on linear OA(4181, 4097, F4, 41) (dual of [4097, 3916, 42]-code), using
(149, 190, 1354087)-Net in Base 4 — Upper bound on s
There is no (149, 190, 1354088)-net in base 4, because
- 1 times m-reduction [i] would yield (149, 189, 1354088)-net in base 4, but
- the generalized Rao bound for nets shows that 4m ≥ 615661 457195 036688 564375 621872 574018 906550 364440 889978 873715 043464 804488 992335 104002 853402 719298 598394 543058 494606 > 4189 [i]