Best Known (119−46, 119, s)-Nets in Base 16
(119−46, 119, 559)-Net over F16 — Constructive and digital
Digital (73, 119, 559)-net over F16, using
- (u, u+v)-construction [i] based on
- digital (4, 27, 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
- digital (46, 92, 514)-net over F16, using
- trace code for nets [i] based on digital (0, 46, 257)-net over F256, using
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- generalized Faure sequence [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F256 with g(F) = 0 and N(F) ≥ 257, using
- the rational function field F256(x) [i]
- Niederreiter sequence [i]
- net from sequence [i] based on digital (0, 256)-sequence over F256, using
- trace code for nets [i] based on digital (0, 46, 257)-net over F256, using
- digital (4, 27, 45)-net over F16, using
(119−46, 119, 1819)-Net over F16 — Digital
Digital (73, 119, 1819)-net over F16, using
- embedding of OOA with Gilbert–Varšamov bound [i] based on linear OA(16119, 1819, F16, 46) (dual of [1819, 1700, 47]-code), using
- 1699 step Varšamov–Edel lengthening with (ri) = (5, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 53 times 0, 1, 55 times 0, 1, 60 times 0, 1, 64 times 0, 1, 67 times 0, 1, 72 times 0, 1, 77 times 0, 1, 82 times 0, 1, 87 times 0, 1, 93 times 0, 1, 99 times 0, 1, 106 times 0) [i] based on linear OA(1646, 47, F16, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,16)), using
- dual of repetition code with length 47 [i]
- 1699 step Varšamov–Edel lengthening with (ri) = (5, 2, 1, 1, 1, 1, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 4 times 0, 1, 6 times 0, 1, 5 times 0, 1, 6 times 0, 1, 7 times 0, 1, 7 times 0, 1, 7 times 0, 1, 9 times 0, 1, 9 times 0, 1, 9 times 0, 1, 11 times 0, 1, 11 times 0, 1, 12 times 0, 1, 13 times 0, 1, 14 times 0, 1, 15 times 0, 1, 16 times 0, 1, 17 times 0, 1, 18 times 0, 1, 20 times 0, 1, 21 times 0, 1, 22 times 0, 1, 24 times 0, 1, 26 times 0, 1, 27 times 0, 1, 29 times 0, 1, 32 times 0, 1, 33 times 0, 1, 36 times 0, 1, 38 times 0, 1, 40 times 0, 1, 44 times 0, 1, 46 times 0, 1, 49 times 0, 1, 53 times 0, 1, 55 times 0, 1, 60 times 0, 1, 64 times 0, 1, 67 times 0, 1, 72 times 0, 1, 77 times 0, 1, 82 times 0, 1, 87 times 0, 1, 93 times 0, 1, 99 times 0, 1, 106 times 0) [i] based on linear OA(1646, 47, F16, 46) (dual of [47, 1, 47]-code or 47-arc in PG(45,16)), using
(119−46, 119, 1067510)-Net in Base 16 — Upper bound on s
There is no (73, 119, 1067511)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 195112 932969 269247 039580 190097 257559 231998 905334 759072 356755 204617 184619 569411 491074 142102 464628 739128 795128 988111 146770 061778 679194 896068 106096 > 16119 [i]