MinT - Best Known (230−55, 230, s)-Nets in Base 4

Best Known (230−55, 230, s)-Nets in Base 4

(230−55, 230, 1036)-Net over F₄ — Constructive and digital

Digital (175, 230, 1036)-net over F₄, using

4² times duplication [i] based on digital (173, 228, 1036)-net over F₄, using
- trace code for nets [i] based on digital (2, 57, 259)-net over F₂₅₆, using
  - net from sequence [i] based on digital (2, 258)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(230−55, 230, 2590)-Net over F₄ — Digital

Digital (175, 230, 2590)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(230−55, 230, 465184)-Net in Base 4 — Upper bound on s

There is no (175, 230, 465185)-net in base 4, because

1 times m-reduction [i] would yield (175, 229, 465185)-net in base 4, but
- 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]