MinT - Best Known (229−54, 229, s)-Nets in Base 4

Best Known (229−54, 229, s)-Nets in Base 4

(229−54, 229, 1040)-Net over F₄ — Constructive and digital

Digital (175, 229, 1040)-net over F₄, using

4¹ times duplication [i] based on digital (174, 228, 1040)-net over F₄, using
- trace code for nets [i] based on digital (3, 57, 260)-net over F₂₅₆, using
  - net from sequence [i] based on digital (3, 259)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(229−54, 229, 2768)-Net over F₄ — Digital

Digital (175, 229, 2768)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−54, 229, 465184)-Net in Base 4 — Upper bound on s

There is no (175, 229, 465185)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 744285 541336 941807 404390 339639 286273 657904 983606 397028 627934 041037 442042 853075 166913 808412 958810 637503 953985 585536 210143 535931 647851 689120 > 4²²⁹ [i]