MinT - Best Known (137−33, 137, s)-Nets in Base 4

Best Known (137−33, 137, s)-Nets in Base 4

(137−33, 137, 1032)-Net over F₄ — Constructive and digital

Digital (104, 137, 1032)-net over F₄, using

4¹ times duplication [i] based on digital (103, 136, 1032)-net over F₄, using
- trace code for nets [i] based on digital (1, 34, 258)-net over F₂₅₆, using
  - net from sequence [i] based on digital (1, 257)-sequence over F₂₅₆, using
    - Niederreiter sequence [i]

(137−33, 137, 1628)-Net over F₄ — Digital

Digital (104, 137, 1628)-net over F₄, using

Gilbertâ€“VarÅ¡amov bound [i]

(137−33, 137, 297104)-Net in Base 4 — Upper bound on s

There is no (104, 137, 297105)-net in base 4, because

1 times m-reduction [i] would yield (104, 136, 297105)-net in base 4, but
- the generalized Rao bound for nets shows that 4^mÂ â‰¥ 7588 920220 261647 735354 271324 121339 114706 469774 892622 285963 138321 976164 500715 559129 > 4¹³⁶ [i]