Best Known (126−96, 126, s)-Nets in Base 16
(126−96, 126, 65)-Net over F16 — Constructive and digital
Digital (30, 126, 65)-net over F16, using
- t-expansion [i] based on digital (6, 126, 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
(126−96, 126, 66)-Net in Base 16 — Constructive
(30, 126, 66)-net in base 16, using
- t-expansion [i] based on (25, 126, 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
(126−96, 126, 162)-Net over F16 — Digital
Digital (30, 126, 162)-net over F16, using
- net from sequence [i] based on digital (30, 161)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 30 and N(F) ≥ 162, using
(126−96, 126, 1782)-Net in Base 16 — Upper bound on s
There is no (30, 126, 1783)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 52 780217 404826 405615 404019 988011 503700 484897 137399 344695 608059 738750 573329 371919 323010 744970 055479 874648 980475 609726 318493 617194 678639 736137 422293 751811 > 16126 [i]