Best Known (113−86, 113, s)-Nets in Base 16
(113−86, 113, 65)-Net over F16 — Constructive and digital
Digital (27, 113, 65)-net over F16, using
- t-expansion [i] based on digital (6, 113, 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
(113−86, 113, 66)-Net in Base 16 — Constructive
(27, 113, 66)-net in base 16, using
- t-expansion [i] based on (25, 113, 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
(113−86, 113, 156)-Net over F16 — Digital
Digital (27, 113, 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
(113−86, 113, 1619)-Net in Base 16 — Upper bound on s
There is no (27, 113, 1620)-net in base 16, because
- the generalized Rao bound for nets shows that 16m ≥ 11805 081202 735589 682951 026500 472504 802823 114722 248848 475033 760901 118136 259362 835302 874863 243324 381797 416517 570843 764762 114386 300753 877276 > 16113 [i]