Best Known (28, 44, s)-Nets in Base 4
(28, 44, 130)-Net over F4 — Constructive and digital
Digital (28, 44, 130)-net over F4, using
- trace code for nets [i] based on digital (6, 22, 65)-net over F16, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- the Hermitian function field over F16 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 6 and N(F) ≥ 65, using
- net from sequence [i] based on digital (6, 64)-sequence over F16, using
(28, 44, 133)-Net over F4 — Digital
Digital (28, 44, 133)-net over F4, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(444, 133, F4, 16) (dual of [133, 89, 17]-code), using
- 39 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 6 times 0, 1, 8 times 0, 1, 9 times 0) [i] based on linear OA(435, 85, F4, 16) (dual of [85, 50, 17]-code), using
- a “GraCyc†code from Grassl’s database [i]
- 39 step Varšamov–Edel lengthening with (ri) = (3, 1, 0, 1, 0, 0, 0, 1, 5 times 0, 1, 6 times 0, 1, 8 times 0, 1, 9 times 0) [i] based on linear OA(435, 85, F4, 16) (dual of [85, 50, 17]-code), using
(28, 44, 2563)-Net in Base 4 — Upper bound on s
There is no (28, 44, 2564)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 309 836009 889448 696207 906240 > 444 [i]