Best Known (20, 20+12, s)-Nets in Base 4
(20, 20+12, 90)-Net over F4 — Constructive and digital
Digital (20, 32, 90)-net over F4, using
- trace code for nets [i] based on digital (4, 16, 45)-net over F16, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 4 and N(F) ≥ 45, using
- net from sequence [i] based on digital (4, 44)-sequence over F16, using
(20, 20+12, 102)-Net over F4 — Digital
Digital (20, 32, 102)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(432, 102, F4, 12) (dual of [102, 70, 13]-code), using
- 12 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 5 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]
- 12 step Varšamov–Edel lengthening with (ri) = (2, 1, 0, 1, 0, 0, 1, 5 times 0) [i] based on linear OA(427, 85, F4, 12) (dual of [85, 58, 13]-code), using
(20, 20+12, 1617)-Net in Base 4 — Upper bound on s
There is no (20, 32, 1618)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 18 471205 125119 975320 > 432 [i]