Best Known (125−98, 125, s)-Nets in Base 16
(125−98, 125, 65)-Net over F16 — Constructive and digital
Digital (27, 125, 65)-net over F16, using
- t-expansion [i] based on digital (6, 125, 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
(125−98, 125, 66)-Net in Base 16 — Constructive
(27, 125, 66)-net in base 16, using
- t-expansion [i] based on (25, 125, 66)-net in base 16, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- T6 from the second tower of function fields by GarcÃa and Stichtenoth over F4 [i]
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 49 and N(F) ≥ 66, using
- t-expansion [i] based on digital (49, 65)-sequence over F4, using
- base expansion [i] based on digital (50, 65)-sequence over F4, using
- net from sequence [i] based on (25, 65)-sequence in base 16, using
(125−98, 125, 156)-Net over F16 — Digital
Digital (27, 125, 156)-net over F16, using
- net from sequence [i] based on digital (27, 155)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 27 and N(F) ≥ 156, using
(125−98, 125, 1475)-Net in Base 16 — Upper bound on s
There is no (27, 125, 1476)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 3 291636 933133 847441 476027 004884 261871 624256 090737 108674 977555 750285 605799 938390 170975 440397 899102 574276 425481 655453 587928 706015 212093 890645 818412 364836 > 16125 [i]