MinT - Best Known (174−42, 174, s)-Nets in Base 4

Best Known (174−42, 174, s)-Nets in Base 4

(174−42, 174, 1032)-Net over F₄ — Constructive and digital

Digital (132, 174, 1032)-net over F₄, using

4² times duplication [i] based on digital (130, 172, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 43, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(174−42, 174, 1952)-Net over F₄ — Digital

Digital (132, 174, 1952)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(174−42, 174, 281735)-Net in Base 4 — Upper bound on s

There is no (132, 174, 281736)-net in base 4, because

the generalized Rao bound for nets shows that 4^mÂ â‰¥ 573 379224 035455 139626 596892 900614 258778 320734 903472 069606 626512 104380 054056 064582 359117 462725 553180 680904 > 4¹⁷⁴ [i]