Best Known (163, 163+88, s)-Nets in Base 4
(163, 163+88, 200)-Net over F4 — Constructive and digital
Digital (163, 251, 200)-net over F4, using
- t-expansion [i] based on digital (161, 251, 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
(163, 163+88, 240)-Net in Base 4 — Constructive
(163, 251, 240)-net in base 4, using
- 41 times duplication [i] based on (162, 250, 240)-net in base 4, using
- t-expansion [i] based on (161, 250, 240)-net in base 4, using
- trace code for nets [i] based on (36, 125, 120)-net in base 16, using
- base change [i] based on digital (11, 100, 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, 100, 120)-net over F32, using
- trace code for nets [i] based on (36, 125, 120)-net in base 16, using
- t-expansion [i] based on (161, 250, 240)-net in base 4, using
(163, 163+88, 563)-Net over F4 — Digital
Digital (163, 251, 563)-net over F4, using
(163, 163+88, 15605)-Net in Base 4 — Upper bound on s
There is no (163, 251, 15606)-net in base 4, because
- the generalized Rao bound for nets shows that 4m ≥ 13 114772 785921 610355 612930 987421 767308 195128 257054 927842 383085 852708 776949 768292 571003 958481 053010 091736 766412 383202 258020 471263 678249 253477 125641 244578 > 4251 [i]