MinT - Best Known (229−55, 229, s)-Nets in Base 4

Best Known (229−55, 229, s)-Nets in Base 4

(229−55, 229, 1036)-Net over F₄ — Constructive and digital

Digital (174, 229, 1036)-net over F₄, using

4¹ 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]

(229−55, 229, 2525)-Net over F₄ — Digital

Digital (174, 229, 2525)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(229−55, 229, 441902)-Net in Base 4 — Upper bound on s

There is no (174, 229, 441903)-net in base 4, because

1 times m-reduction [i] would yield (174, 228, 441903)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 186081 192816 887124 976317 495263 393456 799805 352270 968124 453522 175459 141976 665476 226021 552779 967888 166016 062767 759048 656792 797708 340425 369216 > 4²²⁸ [i]