Best Known (257−90, 257, s)-Nets in Base 4
(257−90, 257, 200)-Net over F4 — Constructive and digital
Digital (167, 257, 200)-net over F4, using
- t-expansion [i] based on digital (161, 257, 200)-net over F4, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F4 with g(F) = 161 and N(F) ≥ 200, using
- F7 from the 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) = 161 and N(F) ≥ 200, using
- net from sequence [i] based on digital (161, 199)-sequence over F4, using
(257−90, 257, 240)-Net in Base 4 — Constructive
(167, 257, 240)-net in base 4, using
- 3 times m-reduction [i] based on (167, 260, 240)-net in base 4, using
- trace code for nets [i] based on (37, 130, 120)-net in base 16, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- Niederreiter–Xing sequence construction II/III [i] based on function field F/F32 with g(F) = 11 and N(F) ≥ 120, using
- net from sequence [i] based on digital (11, 119)-sequence over F32, using
- base change [i] based on digital (11, 104, 120)-net over F32, using
- trace code for nets [i] based on (37, 130, 120)-net in base 16, using
(257−90, 257, 577)-Net over F4 — Digital
Digital (167, 257, 577)-net over F4, using
(257−90, 257, 16087)-Net in Base 4 — Upper bound on s
There is no (167, 257, 16088)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 53714 654793 879933 947386 128537 546820 456569 346805 299074 019339 245471 422193 691993 308115 045227 683575 372937 943909 649847 134284 036543 765588 204493 735028 814112 294348 > 4257 [i]