MinT - Best Known (185−45, 185, s)-Nets in Base 4

Best Known (185−45, 185, s)-Nets in Base 4

(185−45, 185, 1032)-Net over F₄ — Constructive and digital

Digital (140, 185, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (139, 184, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 46, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(185−45, 185, 1977)-Net over F₄ — Digital

Digital (140, 185, 1977)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(185−45, 185, 327430)-Net in Base 4 — Upper bound on s

There is no (140, 185, 327431)-net in base 4, because

1 times m-reduction [i] would yield (140, 184, 327431)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 601 252428 754943 769677 612833 266968 909931 284415 836246 038874 236896 695224 958613 700849 482569 431554 641135 062910 468944 > 4¹⁸⁴ [i]