Best Known (26, 108, s)-Nets in Base 16
(26, 108, 65)-Net over F16 — Constructive and digital
Digital (26, 108, 65)-net over F16, using
- t-expansion [i] based on digital (6, 108, 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
(26, 108, 66)-Net in Base 16 — Constructive
(26, 108, 66)-net in base 16, using
- t-expansion [i] based on (25, 108, 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
(26, 108, 150)-Net over F16 — Digital
Digital (26, 108, 150)-net over F16, using
- net from sequence [i] based on digital (26, 149)-sequence over F16, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F16 with g(F) = 26 and N(F) ≥ 150, using
(26, 108, 1575)-Net in Base 16 — Upper bound on s
There is no (26, 108, 1576)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 11200 558422 405908 656167 490792 589062 145437 900611 807088 952598 573704 521340 875516 558950 544475 347051 631004 064497 169158 209915 670588 615616 > 16108 [i]