Best Known (51, 115, s)-Nets in Base 16
(51, 115, 243)-Net over F16 — Constructive and digital
Digital (51, 115, 243)-net over F16, using
- t-expansion [i] based on digital (48, 115, 243)-net over F16, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 48 and N(F) ≥ 243, using
- net from sequence [i] based on digital (48, 242)-sequence over F16, using
(51, 115, 255)-Net over F16 — Digital
Digital (51, 115, 255)-net over F16, using
- t-expansion [i] based on digital (50, 115, 255)-net over F16, using
- net from sequence [i] based on digital (50, 254)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 50 and N(F) ≥ 255, using
- net from sequence [i] based on digital (50, 254)-sequence over F16, using
(51, 115, 257)-Net in Base 16
(51, 115, 257)-net in base 16, using
- base change [i] based on digital (28, 92, 257)-net over F32, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 28 and N(F) ≥ 257, using
- net from sequence [i] based on digital (28, 256)-sequence over F32, using
(51, 115, 18099)-Net in Base 16 — Upper bound on s
There is no (51, 115, 18100)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 2 978462 669274 033696 756138 121199 052186 370055 859030 598229 666993 290756 606302 708605 820677 836417 661426 171822 562931 443234 476148 818643 061402 199251 > 16115 [i]