Best Known (119, 119+40, s)-Nets in Base 4
(119, 119+40, 531)-Net over F4 — Constructive and digital
Digital (119, 159, 531)-net over F4, using
- 9 times m-reduction [i] based on digital (119, 168, 531)-net over F4, using
- trace code for nets [i] based on digital (7, 56, 177)-net over F64, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F64 with g(F) = 7 and N(F) ≥ 177, using
- net from sequence [i] based on digital (7, 176)-sequence over F64, using
- trace code for nets [i] based on digital (7, 56, 177)-net over F64, using
(119, 119+40, 648)-Net in Base 4 — Constructive
(119, 159, 648)-net in base 4, using
- trace code for nets [i] based on (13, 53, 216)-net in base 64, using
- 3 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F128 with g(F) = 5 and N(F) ≥ 216, using
- net from sequence [i] based on digital (5, 215)-sequence over F128, using
- base change [i] based on digital (5, 48, 216)-net over F128, using
- 3 times m-reduction [i] based on (13, 56, 216)-net in base 64, using
(119, 119+40, 1481)-Net over F4 — Digital
Digital (119, 159, 1481)-net over F4, using
(119, 119+40, 169246)-Net in Base 4 — Upper bound on s
There is no (119, 159, 169247)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 534010 356190 171570 545475 390853 684111 958909 573544 238010 059645 147252 390235 399580 109547 049038 926071 > 4159 [i]