Best Known (34−12, 34, s)-Nets in Base 4
(34−12, 34, 98)-Net over F4 — Constructive and digital
Digital (22, 34, 98)-net over F4, using
- trace code for nets [i] based on digital (5, 17, 49)-net over F16, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 5 and N(F) ≥ 49, using
- net from sequence [i] based on digital (5, 48)-sequence over F16, using
(34−12, 34, 125)-Net over F4 — Digital
Digital (22, 34, 125)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(434, 125, F4, 12) (dual of [125, 91, 13]-code), using
- 33 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 8 times 0, 1, 11 times 0) [i] based on linear OA(427, 85, F4, 12) (dual of [85, 58, 13]-code), using
- a “GraCyc†code from Grassl’s database [i]
- 33 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 5 times 0, 1, 8 times 0, 1, 11 times 0) [i] based on linear OA(427, 85, F4, 12) (dual of [85, 58, 13]-code), using
(34−12, 34, 2570)-Net in Base 4 — Upper bound on s
There is no (22, 34, 2571)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 295 502505 579756 222274 > 434 [i]