MinT - Best Known (243−55, 243, s)-Nets in Base 4

Best Known (243−55, 243, s)-Nets in Base 4

(243−55, 243, 1048)-Net over F₄ — Constructive and digital

Digital (188, 243, 1048)-net over F₄, using

1 times m-reduction [i] based on digital (188, 244, 1048)-net over F₄, using
- trace code for nets [i] based on digital (5, 61, 262)-net over F₂₅₆, using
  - net from sequence [i] based on digital (5, 261)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(243−55, 243, 3605)-Net over F₄ — Digital

Digital (188, 243, 3605)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(243−55, 243, 906810)-Net in Base 4 — Upper bound on s

There is no (188, 243, 906811)-net in base 4, because

1 times m-reduction [i] would yield (188, 242, 906811)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 49 949208 723835 853652 745339 681631 318559 268805 360476 291400 979280 215991 330006 848096 725480 190873 758268 904413 304844 317667 089692 387512 176412 550761 722180 > 4²⁴² [i]